Let A and B be the following matrices A 1 1 9 5 6 1 9 9 1 B

Let A and B be the following matrices. A = [1 1 -9 5 6 1 -9 9 1], B = [1 5 -7 -8 -6 2 -5 -5 -4] Perform the following operations: -104 = [] A + 7B = [] 5A - 2B = []

Solution

Here rule is that in multiplying a number by a matrix, we multiply its each element by that number.

So clearly

-10A = [-10 x 1 -10 x 1           -10 x (-9) ]      

           [ -10 x 5    -10 x 6            -10 x 1 ]          

          [-10 x (-9)      -10 x 9           -10 x 1 ]

= [ -10, -10, 90]

   [ -50 -60 -10 ]

   [ 90 -90 -10 ]

This is the answer of part (a).

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Accordingly

7B = 7 [ 1   5   -7 ]

           [ -8 -6   2 ]

           [ -5 -5 -4 ]

=    [ 1x7    5x7 -7 x7]

           [ -8x7 -6x7    2x7 ]

           [ -5x7 -5x7 -4x7 ]

= [ 7     35       -49 ]

   [ -56   -42      14 ]

   [ -35   -35     -28 ]

so clearly A + 7B

=[ 1    1   -9 ] [ 7     35       -49 ]

[ 5    6 1] + [ -56   -42      14 ]

[ -9 9 1 ]    [ -35   -35     -28 ]

=[ 1+7           1+35        -9-49]

[ 5 - 56         6 -42        1+14]

[ -9-35          9-35         1-28 ]

= [ 6           36        -58]

   [ -51        -36       15 ]

   [ -44        -26      -27 ]

This is the answer of part (b)

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Again

5A - 2 B= [ 1    1   -9 ]            [ 1   5   -7 ]

         5 [ 5    6 1]       - 2 [ -8 -6   2 ]

      [ -9 9 1 ]          [ -5 -5 -4 ]

= [ 5         5   -45 ]           [ 2   10   -14]

   [ 25     30     5 ]   -       [ -16 -12 4 ]

   [ -45    45     5 ]           [ -10 -10 -8]       ( it is on multiplying each outside number by each inside number)

Now on subtracting corresponding numbers, we get

= [ 5 -2            5-10        -45 +14 ]

   [ 25+16       30+12        5-4      ]

   [ -45+ 10     45+10         5+8    ]

=[ 3     -5      -31]

[41    42      1 ]

[ -35   55      13 ]

This is the last answer for part (c).