Start with the following matrix 4 2 10 83 4 8 3 9 1 9 1 Perf

Start with the following matrix: [4 -2 -10 8-3 4 8 3 -9 1 9 1] Perform the following 3 elementary row operations, one after the other, and give the resulting matrix at each step: Add 2 times row 4 to row 1 [0 0 0 0 0 0 0 0 0] Multiply row 2 by 6 [0 0 0 0 0 0 0 0 0] Interchange rows 2 and 3 [0 0 0 0 0 0 0 0 0]

Solution

Given Matrix

          4          -2           -10

          8          -3             4

          8           3            -9

          1           9             1

a)

add 2 times row 4 to row 1

i.e. we need to add 2 times of row 4 to row 1

R₁ -> 2R₄ + R₁                                                         2R₄ =        2        18          2

          6          16           -8

          8          -3             4

          8           3            -9

          1           9             1

b)

our new matrix from (a) is      

          6          16           -8

          8          -3             4

          8           3            -9

          1           9             1

multiply row 2 by 6

now we have to multiply every element of row 2 by 6

R₂ -> 6*R₂

          6           16         -8

         48         -18          24

          8           3            -9

          1           9             1

c)

now we have to interchange elements of row 2 to row 3 and elements of row 3 to row 2.

we have our new matrix from (b)

          6           16         -8

         48         -18          24

          8           3            -9

          1           9             1

R₂ <-> R₃

         6           16         -8

         8            3           -9

         48         -18         24

          1            9            1