E2 - Row Reduction


Example 1

E2 - Row Reduction (ver. 1)

Show how to compute \(\operatorname{RREF}(A)\) given \(A=\left[\begin{array}{rrr} -1 & 1 & 0 \\ 0 & 1 & 1 \\ -4 & 12 & 8 \\ -2 & 3 & 1 \\ -2 & 5 & 3 \end{array}\right]\).

Answer.

\(\left[\begin{array}{rrr} 1 & 0 & 1 \\ 0 & 1 & 1 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}\right]\)


Example 2

E2 - Row Reduction (ver. 2)

Show how to compute \(\operatorname{RREF}(A)\) given \(A=\left[\begin{array}{rrr} 1 & 5 & 7 \\ 0 & 1 & 2 \\ 0 & 4 & 8 \\ 2 & 8 & 10 \\ -2 & -7 & -8 \end{array}\right]\).

Answer.

\(\left[\begin{array}{rrr} 1 & 0 & -3 \\ 0 & 1 & 2 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}\right]\)


Example 3

E2 - Row Reduction (ver. 3)

Show how to compute \(\operatorname{RREF}(A)\) given \(A=\left[\begin{array}{rrrr} 1 & 1 & 0 & 2 \\ -3 & -2 & -1 & -7 \\ 0 & 0 & 1 & 2 \\ 0 & -2 & -5 & -12 \end{array}\right]\).

Answer.

\(\left[\begin{array}{rrrr} 1 & 0 & 0 & 1 \\ 0 & 1 & 0 & 1 \\ 0 & 0 & 1 & 2 \\ 0 & 0 & 0 & 0 \end{array}\right]\)


Example 4

E2 - Row Reduction (ver. 4)

Show how to compute \(\operatorname{RREF}(A)\) given \(A=\left[\begin{array}{rrrr} 0 & -1 & 0 & 2 \\ 1 & 0 & 1 & -2 \\ 2 & 0 & 2 & -4 \\ -3 & 7 & -3 & -8 \end{array}\right]\).

Answer.

\(\left[\begin{array}{rrrr} 1 & 0 & 1 & -2 \\ 0 & 1 & 0 & -2 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \end{array}\right]\)


Example 5

E2 - Row Reduction (ver. 5)

Show how to compute \(\operatorname{RREF}(A)\) given \(A=\left[\begin{array}{rrrrr} -1 & -3 & 11 & 6 & 0 \\ 3 & 1 & -1 & -10 & 8 \\ -2 & -3 & 10 & 9 & -3 \end{array}\right]\).

Answer.

\(\left[\begin{array}{rrrrr} 1 & 0 & 1 & -3 & 3 \\ 0 & 1 & -4 & -1 & -1 \\ 0 & 0 & 0 & 0 & 0 \end{array}\right]\)


Example 6

E2 - Row Reduction (ver. 6)

Show how to compute \(\operatorname{RREF}(A)\) given \(A=\left[\begin{array}{rrr} 1 & 4 & 1 \\ -5 & -9 & -5 \\ -2 & 0 & -2 \\ 1 & -3 & 1 \\ 0 & 2 & 0 \end{array}\right]\).

Answer.

\(\left[\begin{array}{rrr} 1 & 0 & 1 \\ 0 & 1 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}\right]\)


Example 7

E2 - Row Reduction (ver. 7)

Show how to compute \(\operatorname{RREF}(A)\) given \(A=\left[\begin{array}{rrr} -1 & -1 & -4 \\ -1 & -2 & -7 \\ -1 & -2 & -7 \\ -2 & -2 & -8 \\ 1 & 0 & 1 \end{array}\right]\).

Answer.

\(\left[\begin{array}{rrr} 1 & 0 & 1 \\ 0 & 1 & 3 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}\right]\)


Example 8

E2 - Row Reduction (ver. 8)

Show how to compute \(\operatorname{RREF}(A)\) given \(A=\left[\begin{array}{rrr} -2 & -10 & 2 \\ 2 & 10 & 11 \\ -2 & -10 & -9 \\ -2 & -10 & -9 \\ 1 & 5 & 1 \end{array}\right]\).

Answer.

\(\left[\begin{array}{rrr} 1 & 5 & 0 \\ 0 & 0 & 1 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}\right]\)


Example 9

E2 - Row Reduction (ver. 9)

Show how to compute \(\operatorname{RREF}(A)\) given \(A=\left[\begin{array}{rrrr} -1 & 5 & -3 & -4 \\ 0 & 0 & 1 & 1 \\ 1 & -5 & 5 & 6 \\ -2 & 10 & -6 & -8 \end{array}\right]\).

Answer.

\(\left[\begin{array}{rrrr} 1 & -5 & 0 & 1 \\ 0 & 0 & 1 & 1 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \end{array}\right]\)


Example 10

E2 - Row Reduction (ver. 10)

Show how to compute \(\operatorname{RREF}(A)\) given \(A=\left[\begin{array}{rrr} -1 & 1 & -4 \\ 1 & -2 & 7 \\ -1 & 3 & -10 \\ 1 & -1 & 4 \\ 0 & 0 & 0 \end{array}\right]\).

Answer.

\(\left[\begin{array}{rrr} 1 & 0 & 1 \\ 0 & 1 & -3 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}\right]\)


Example 11

E2 - Row Reduction (ver. 11)

Show how to compute \(\operatorname{RREF}(A)\) given \(A=\left[\begin{array}{rrrr} -1 & 5 & -8 & 11 \\ 0 & 0 & 1 & -1 \\ -1 & 5 & -3 & 6 \\ -1 & 5 & 4 & -1 \end{array}\right]\).

Answer.

\(\left[\begin{array}{rrrr} 1 & -5 & 0 & -3 \\ 0 & 0 & 1 & -1 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \end{array}\right]\)


Example 12

E2 - Row Reduction (ver. 12)

Show how to compute \(\operatorname{RREF}(A)\) given \(A=\left[\begin{array}{rrrr} 1 & -2 & -6 & 7 \\ 0 & 1 & 3 & -4 \\ 0 & 2 & 7 & -10 \\ 0 & -3 & -5 & 4 \end{array}\right]\).

Answer.

\(\left[\begin{array}{rrrr} 1 & 0 & 0 & -1 \\ 0 & 1 & 0 & 2 \\ 0 & 0 & 1 & -2 \\ 0 & 0 & 0 & 0 \end{array}\right]\)


Example 13

E2 - Row Reduction (ver. 13)

Show how to compute \(\operatorname{RREF}(A)\) given \(A=\left[\begin{array}{rrrrr} 1 & -4 & 2 & -1 & -1 \\ 3 & -12 & 7 & -3 & -4 \\ 3 & -12 & 2 & -3 & 1 \end{array}\right]\).

Answer.

\(\left[\begin{array}{rrrrr} 1 & -4 & 0 & -1 & 1 \\ 0 & 0 & 1 & 0 & -1 \\ 0 & 0 & 0 & 0 & 0 \end{array}\right]\)


Example 14

E2 - Row Reduction (ver. 14)

Show how to compute \(\operatorname{RREF}(A)\) given \(A=\left[\begin{array}{rrrrr} -1 & 4 & 7 & 7 & 4 \\ -1 & 3 & 6 & 5 & 3 \\ -2 & 2 & 8 & 2 & 2 \end{array}\right]\).

Answer.

\(\left[\begin{array}{rrrrr} 1 & 0 & -3 & 1 & 0 \\ 0 & 1 & 1 & 2 & 1 \\ 0 & 0 & 0 & 0 & 0 \end{array}\right]\)


Example 15

E2 - Row Reduction (ver. 15)

Show how to compute \(\operatorname{RREF}(A)\) given \(A=\left[\begin{array}{rrr} 1 & 2 & -7 \\ -2 & -3 & 10 \\ 1 & -1 & 5 \\ -1 & 0 & -1 \\ 2 & 2 & -6 \end{array}\right]\).

Answer.

\(\left[\begin{array}{rrr} 1 & 0 & 1 \\ 0 & 1 & -4 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}\right]\)


Example 16

E2 - Row Reduction (ver. 16)

Show how to compute \(\operatorname{RREF}(A)\) given \(A=\left[\begin{array}{rrrr} 1 & -5 & -9 & 11 \\ 1 & -4 & -8 & 10 \\ 1 & 0 & -3 & 4 \\ -1 & 5 & 6 & -5 \end{array}\right]\).

Answer.

\(\left[\begin{array}{rrrr} 1 & 0 & 0 & -2 \\ 0 & 1 & 0 & 1 \\ 0 & 0 & 1 & -2 \\ 0 & 0 & 0 & 0 \end{array}\right]\)


Example 17

E2 - Row Reduction (ver. 17)

Show how to compute \(\operatorname{RREF}(A)\) given \(A=\left[\begin{array}{rrrr} 1 & -3 & -5 & 10 \\ 1 & -2 & -4 & 7 \\ 1 & 1 & -1 & -2 \\ 0 & -2 & -2 & 6 \end{array}\right]\).

Answer.

\(\left[\begin{array}{rrrr} 1 & 0 & -2 & 1 \\ 0 & 1 & 1 & -3 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \end{array}\right]\)


Example 18

E2 - Row Reduction (ver. 18)

Show how to compute \(\operatorname{RREF}(A)\) given \(A=\left[\begin{array}{rrr} 4 & -4 & 8 \\ -1 & -1 & 0 \\ 1 & -2 & 3 \\ -1 & -6 & 5 \\ 0 & 4 & -4 \end{array}\right]\).

Answer.

\(\left[\begin{array}{rrr} 1 & 0 & 1 \\ 0 & 1 & -1 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}\right]\)


Example 19

E2 - Row Reduction (ver. 19)

Show how to compute \(\operatorname{RREF}(A)\) given \(A=\left[\begin{array}{rrrr} 1 & -2 & -1 & -2 \\ 0 & 1 & 0 & -1 \\ 1 & 8 & 0 & -9 \\ 0 & 3 & 0 & -3 \end{array}\right]\).

Answer.

\(\left[\begin{array}{rrrr} 1 & 0 & 0 & -1 \\ 0 & 1 & 0 & -1 \\ 0 & 0 & 1 & 3 \\ 0 & 0 & 0 & 0 \end{array}\right]\)


Example 20

E2 - Row Reduction (ver. 20)

Show how to compute \(\operatorname{RREF}(A)\) given \(A=\left[\begin{array}{rrrr} 1 & 2 & 6 & -12 \\ 0 & 1 & 1 & -3 \\ 0 & 3 & 4 & -11 \\ 1 & -2 & 6 & -8 \end{array}\right]\).

Answer.

\(\left[\begin{array}{rrrr} 1 & 0 & 0 & 2 \\ 0 & 1 & 0 & -1 \\ 0 & 0 & 1 & -2 \\ 0 & 0 & 0 & 0 \end{array}\right]\)


Example 21

E2 - Row Reduction (ver. 21)

Show how to compute \(\operatorname{RREF}(A)\) given \(A=\left[\begin{array}{rrrrr} 1 & 3 & -1 & -6 & -2 \\ 0 & 1 & -1 & -1 & 0 \\ -1 & -1 & -1 & 4 & 2 \end{array}\right]\).

Answer.

\(\left[\begin{array}{rrrrr} 1 & 0 & 2 & -3 & -2 \\ 0 & 1 & -1 & -1 & 0 \\ 0 & 0 & 0 & 0 & 0 \end{array}\right]\)


Example 22

E2 - Row Reduction (ver. 22)

Show how to compute \(\operatorname{RREF}(A)\) given \(A=\left[\begin{array}{rrrrr} -1 & -1 & -2 & -3 & 2 \\ -1 & -2 & -3 & -5 & 3 \\ 2 & 3 & 5 & 8 & -5 \end{array}\right]\).

Answer.

\(\left[\begin{array}{rrrrr} 1 & 0 & 1 & 1 & -1 \\ 0 & 1 & 1 & 2 & -1 \\ 0 & 0 & 0 & 0 & 0 \end{array}\right]\)


Example 23

E2 - Row Reduction (ver. 23)

Show how to compute \(\operatorname{RREF}(A)\) given \(A=\left[\begin{array}{rrrrr} -1 & -2 & 1 & -4 & -3 \\ 0 & 0 & 1 & -3 & -3 \\ -1 & -2 & 2 & -7 & -6 \end{array}\right]\).

Answer.

\(\left[\begin{array}{rrrrr} 1 & 2 & 0 & 1 & 0 \\ 0 & 0 & 1 & -3 & -3 \\ 0 & 0 & 0 & 0 & 0 \end{array}\right]\)


Example 24

E2 - Row Reduction (ver. 24)

Show how to compute \(\operatorname{RREF}(A)\) given \(A=\left[\begin{array}{rrrr} 1 & 0 & 0 & 1 \\ -4 & 1 & -5 & -6 \\ -2 & -2 & 11 & 2 \\ 5 & 0 & 5 & 5 \end{array}\right]\).

Answer.

\(\left[\begin{array}{rrrr} 1 & 0 & 0 & 1 \\ 0 & 1 & 0 & -2 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 0 \end{array}\right]\)


Example 25

E2 - Row Reduction (ver. 25)

Show how to compute \(\operatorname{RREF}(A)\) given \(A=\left[\begin{array}{rrrr} -2 & 0 & 5 & 6 \\ -1 & 2 & -5 & 5 \\ 3 & -1 & -4 & -10 \\ -2 & 0 & 6 & 6 \end{array}\right]\).

Answer.

\(\left[\begin{array}{rrrr} 1 & 0 & 0 & -3 \\ 0 & 1 & 0 & 1 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 0 \end{array}\right]\)


Example 26

E2 - Row Reduction (ver. 26)

Show how to compute \(\operatorname{RREF}(A)\) given \(A=\left[\begin{array}{rrr} 2 & 7 & 9 \\ 1 & 5 & 6 \\ 0 & 4 & 4 \\ 1 & 3 & 4 \\ -1 & -4 & -5 \end{array}\right]\).

Answer.

\(\left[\begin{array}{rrr} 1 & 0 & 1 \\ 0 & 1 & 1 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}\right]\)


Example 27

E2 - Row Reduction (ver. 27)

Show how to compute \(\operatorname{RREF}(A)\) given \(A=\left[\begin{array}{rrrrr} -1 & -1 & 0 & 0 & 2 \\ 1 & 4 & 3 & 0 & -5 \\ -2 & -4 & -2 & 0 & 6 \end{array}\right]\).

Answer.

\(\left[\begin{array}{rrrrr} 1 & 0 & -1 & 0 & -1 \\ 0 & 1 & 1 & 0 & -1 \\ 0 & 0 & 0 & 0 & 0 \end{array}\right]\)


Example 28

E2 - Row Reduction (ver. 28)

Show how to compute \(\operatorname{RREF}(A)\) given \(A=\left[\begin{array}{rrrr} -1 & 5 & -8 & -2 \\ -1 & -4 & 3 & 0 \\ 1 & 0 & 2 & 1 \\ 2 & 7 & -10 & -5 \end{array}\right]\).

Answer.

\(\left[\begin{array}{rrrr} 1 & 0 & 0 & -1 \\ 0 & 1 & 0 & 1 \\ 0 & 0 & 1 & 1 \\ 0 & 0 & 0 & 0 \end{array}\right]\)


Example 29

E2 - Row Reduction (ver. 29)

Show how to compute \(\operatorname{RREF}(A)\) given \(A=\left[\begin{array}{rrr} -3 & 3 & -3 \\ 1 & -2 & 1 \\ 4 & -11 & 4 \\ -4 & 8 & -4 \\ 2 & -3 & 2 \end{array}\right]\).

Answer.

\(\left[\begin{array}{rrr} 1 & 0 & 1 \\ 0 & 1 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}\right]\)


Example 30

E2 - Row Reduction (ver. 30)

Show how to compute \(\operatorname{RREF}(A)\) given \(A=\left[\begin{array}{rrrr} -2 & 7 & 8 & -1 \\ -3 & 10 & 12 & -1 \\ -2 & 6 & 9 & 1 \\ -2 & 11 & 4 & -9 \end{array}\right]\).

Answer.

\(\left[\begin{array}{rrrr} 1 & 0 & 0 & 1 \\ 0 & 1 & 0 & -1 \\ 0 & 0 & 1 & 1 \\ 0 & 0 & 0 & 0 \end{array}\right]\)


Example 31

E2 - Row Reduction (ver. 31)

Show how to compute \(\operatorname{RREF}(A)\) given \(A=\left[\begin{array}{rrrrr} 2 & 6 & 9 & -9 & 7 \\ 1 & 3 & 6 & -6 & 5 \\ -1 & -3 & -4 & 4 & -3 \end{array}\right]\).

Answer.

\(\left[\begin{array}{rrrrr} 1 & 3 & 0 & 0 & -1 \\ 0 & 0 & 1 & -1 & 1 \\ 0 & 0 & 0 & 0 & 0 \end{array}\right]\)


Example 32

E2 - Row Reduction (ver. 32)

Show how to compute \(\operatorname{RREF}(A)\) given \(A=\left[\begin{array}{rrrr} -5 & -2 & -5 & 10 \\ -2 & -1 & -1 & 5 \\ 3 & 2 & 0 & -9 \\ 1 & -1 & 8 & 5 \end{array}\right]\).

Answer.

\(\left[\begin{array}{rrrr} 1 & 0 & 0 & -3 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 1 \\ 0 & 0 & 0 & 0 \end{array}\right]\)


Example 33

E2 - Row Reduction (ver. 33)

Show how to compute \(\operatorname{RREF}(A)\) given \(A=\left[\begin{array}{rrrrr} 1 & 1 & 1 & 2 & -4 \\ 0 & 1 & 2 & 1 & -2 \\ -1 & 2 & 5 & 1 & -2 \end{array}\right]\).

Answer.

\(\left[\begin{array}{rrrrr} 1 & 0 & -1 & 1 & -2 \\ 0 & 1 & 2 & 1 & -2 \\ 0 & 0 & 0 & 0 & 0 \end{array}\right]\)


Example 34

E2 - Row Reduction (ver. 34)

Show how to compute \(\operatorname{RREF}(A)\) given \(A=\left[\begin{array}{rrrr} 1 & -5 & -2 & -8 \\ -1 & 6 & 3 & 8 \\ -1 & 5 & 3 & 5 \\ 0 & -5 & -6 & 3 \end{array}\right]\).

Answer.

\(\left[\begin{array}{rrrr} 1 & 0 & 0 & 1 \\ 0 & 1 & 0 & 3 \\ 0 & 0 & 1 & -3 \\ 0 & 0 & 0 & 0 \end{array}\right]\)


Example 35

E2 - Row Reduction (ver. 35)

Show how to compute \(\operatorname{RREF}(A)\) given \(A=\left[\begin{array}{rrrrr} -1 & -2 & 3 & -1 & -5 \\ -2 & -4 & 5 & -2 & -9 \\ 0 & 0 & 5 & 0 & -5 \end{array}\right]\).

Answer.

\(\left[\begin{array}{rrrrr} 1 & 2 & 0 & 1 & 2 \\ 0 & 0 & 1 & 0 & -1 \\ 0 & 0 & 0 & 0 & 0 \end{array}\right]\)


Example 36

E2 - Row Reduction (ver. 36)

Show how to compute \(\operatorname{RREF}(A)\) given \(A=\left[\begin{array}{rrr} 0 & 4 & -8 \\ 2 & -1 & 0 \\ 2 & 2 & -6 \\ 1 & -5 & 9 \\ 1 & 1 & -3 \end{array}\right]\).

Answer.

\(\left[\begin{array}{rrr} 1 & 0 & -1 \\ 0 & 1 & -2 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}\right]\)


Example 37

E2 - Row Reduction (ver. 37)

Show how to compute \(\operatorname{RREF}(A)\) given \(A=\left[\begin{array}{rrr} 0 & 0 & 0 \\ 1 & -4 & -6 \\ -1 & 6 & 8 \\ -1 & 2 & 4 \\ 1 & -5 & -7 \end{array}\right]\).

Answer.

\(\left[\begin{array}{rrr} 1 & 0 & -2 \\ 0 & 1 & 1 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}\right]\)


Example 38

E2 - Row Reduction (ver. 38)

Show how to compute \(\operatorname{RREF}(A)\) given \(A=\left[\begin{array}{rrrrr} 1 & 4 & 7 & -5 & 2 \\ 1 & 5 & 9 & -6 & 3 \\ 0 & 0 & 0 & 0 & 0 \end{array}\right]\).

Answer.

\(\left[\begin{array}{rrrrr} 1 & 0 & -1 & -1 & -2 \\ 0 & 1 & 2 & -1 & 1 \\ 0 & 0 & 0 & 0 & 0 \end{array}\right]\)


Example 39

E2 - Row Reduction (ver. 39)

Show how to compute \(\operatorname{RREF}(A)\) given \(A=\left[\begin{array}{rrr} 0 & -5 & 0 \\ -2 & -9 & 4 \\ -2 & -12 & 4 \\ -1 & -10 & 2 \\ -1 & -5 & 2 \end{array}\right]\).

Answer.

\(\left[\begin{array}{rrr} 1 & 0 & -2 \\ 0 & 1 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}\right]\)


Example 40

E2 - Row Reduction (ver. 40)

Show how to compute \(\operatorname{RREF}(A)\) given \(A=\left[\begin{array}{rrrr} -1 & -4 & -5 & 6 \\ 2 & 8 & 7 & -9 \\ 2 & 8 & 8 & -10 \\ 1 & 4 & 4 & -5 \end{array}\right]\).

Answer.

\(\left[\begin{array}{rrrr} 1 & 4 & 0 & -1 \\ 0 & 0 & 1 & -1 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \end{array}\right]\)


Example 41

E2 - Row Reduction (ver. 41)

Show how to compute \(\operatorname{RREF}(A)\) given \(A=\left[\begin{array}{rrrrr} -1 & 0 & 3 & -1 & 2 \\ -4 & -3 & 6 & -10 & 8 \\ 2 & 1 & -4 & 4 & -4 \end{array}\right]\).

Answer.

\(\left[\begin{array}{rrrrr} 1 & 0 & -3 & 1 & -2 \\ 0 & 1 & 2 & 2 & 0 \\ 0 & 0 & 0 & 0 & 0 \end{array}\right]\)


Example 42

E2 - Row Reduction (ver. 42)

Show how to compute \(\operatorname{RREF}(A)\) given \(A=\left[\begin{array}{rrrr} 0 & 1 & -2 & -4 \\ -1 & 1 & 2 & 1 \\ 0 & -1 & 2 & 5 \\ 0 & 1 & -2 & -5 \end{array}\right]\).

Answer.

\(\left[\begin{array}{rrrr} 1 & 0 & -4 & 0 \\ 0 & 1 & -2 & 0 \\ 0 & 0 & 0 & 1 \\ 0 & 0 & 0 & 0 \end{array}\right]\)


Example 43

E2 - Row Reduction (ver. 43)

Show how to compute \(\operatorname{RREF}(A)\) given \(A=\left[\begin{array}{rrrrr} 4 & -4 & 0 & 4 & -8 \\ 2 & -3 & -2 & 3 & -6 \\ 3 & -2 & 2 & 2 & -4 \end{array}\right]\).

Answer.

\(\left[\begin{array}{rrrrr} 1 & 0 & 2 & 0 & 0 \\ 0 & 1 & 2 & -1 & 2 \\ 0 & 0 & 0 & 0 & 0 \end{array}\right]\)


Example 44

E2 - Row Reduction (ver. 44)

Show how to compute \(\operatorname{RREF}(A)\) given \(A=\left[\begin{array}{rrrrr} 1 & 0 & 2 & 0 & 2 \\ 1 & 1 & 1 & -3 & 2 \\ 5 & 3 & 7 & -9 & 10 \end{array}\right]\).

Answer.

\(\left[\begin{array}{rrrrr} 1 & 0 & 2 & 0 & 2 \\ 0 & 1 & -1 & -3 & 0 \\ 0 & 0 & 0 & 0 & 0 \end{array}\right]\)


Example 45

E2 - Row Reduction (ver. 45)

Show how to compute \(\operatorname{RREF}(A)\) given \(A=\left[\begin{array}{rrr} -3 & 7 & -1 \\ 2 & -5 & 1 \\ -2 & 9 & -5 \\ 3 & -9 & 3 \\ 2 & -8 & 4 \end{array}\right]\).

Answer.

\(\left[\begin{array}{rrr} 1 & 0 & -2 \\ 0 & 1 & -1 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}\right]\)


Example 46

E2 - Row Reduction (ver. 46)

Show how to compute \(\operatorname{RREF}(A)\) given \(A=\left[\begin{array}{rrrr} -1 & 1 & -4 & 5 \\ -1 & 0 & -4 & 7 \\ 0 & 2 & 1 & -6 \\ -1 & -2 & 0 & 3 \end{array}\right]\).

Answer.

\(\left[\begin{array}{rrrr} 1 & 0 & 0 & 1 \\ 0 & 1 & 0 & -2 \\ 0 & 0 & 1 & -2 \\ 0 & 0 & 0 & 0 \end{array}\right]\)


Example 47

E2 - Row Reduction (ver. 47)

Show how to compute \(\operatorname{RREF}(A)\) given \(A=\left[\begin{array}{rrr} 1 & -1 & 0 \\ 2 & -7 & 10 \\ 1 & 0 & -2 \\ 0 & -1 & 2 \\ 1 & -6 & 10 \end{array}\right]\).

Answer.

\(\left[\begin{array}{rrr} 1 & 0 & -2 \\ 0 & 1 & -2 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}\right]\)


Example 48

E2 - Row Reduction (ver. 48)

Show how to compute \(\operatorname{RREF}(A)\) given \(A=\left[\begin{array}{rrrrr} 1 & 1 & 4 & -5 & 3 \\ 0 & 0 & 1 & -1 & 1 \\ 2 & 2 & 7 & -9 & 5 \end{array}\right]\).

Answer.

\(\left[\begin{array}{rrrrr} 1 & 1 & 0 & -1 & -1 \\ 0 & 0 & 1 & -1 & 1 \\ 0 & 0 & 0 & 0 & 0 \end{array}\right]\)


Example 49

E2 - Row Reduction (ver. 49)

Show how to compute \(\operatorname{RREF}(A)\) given \(A=\left[\begin{array}{rrrr} 1 & 0 & -1 & -3 \\ -1 & 1 & 2 & 5 \\ -4 & -3 & 1 & 6 \\ -4 & -5 & -1 & 2 \end{array}\right]\).

Answer.

\(\left[\begin{array}{rrrr} 1 & 0 & -1 & -3 \\ 0 & 1 & 1 & 2 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \end{array}\right]\)


Example 50

E2 - Row Reduction (ver. 50)

Show how to compute \(\operatorname{RREF}(A)\) given \(A=\left[\begin{array}{rrrr} 4 & -8 & 4 & 0 \\ 2 & -3 & 1 & 1 \\ -1 & 7 & -6 & 5 \\ -1 & 2 & -1 & 0 \end{array}\right]\).

Answer.

\(\left[\begin{array}{rrrr} 1 & 0 & -1 & 2 \\ 0 & 1 & -1 & 1 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \end{array}\right]\)