Question

Find the value of `a,b` and `c`, wherever applicable, in following matrix operations?

(a) `((2,1,a),(-9,b,4),(1,0,5))-((3,5,1),(7,1,c),(3,-1,6))=((-1,-4,7),(-16,-1,-5),(-2,1,-1))`
(b) `((3,1,10),(0,-5,4),(-2,2,-1))xxa=((-9,-3,-30),(0,15,-12),(6,-6,3))`

Answer 1

(a) `a=8`, `b=0` and `c=9`
(b) `a=-3`

Explanation:

(a) `((2,1,a),(-9,b,4),(1,0,5))-((3,5,1),(7,1,c),(3,-1,6))=((-1,-4,7),(-16,-1,-5),(-2,1,-1))`

This is a subtracting a matrix from another. In doing so, we subtract

from first element from first row of first matrix, which is `2`, first element from first row of second matrix, which is `3`, o get first element of first row of resultant matrix, which is `2-3=-1`.

Similarly we have for second element of first row i.e. `1-5=-4`.

We should also have this for third element of first row too i.e. `a-1=7`. Adding `1` on each side we get `a=8`.

`b` is in second element of second row and we ought to have `b-1=-1` and adding `1` on each side we get `b=-1+1=0`

`c` is third element of second row (in second matrix) and we ought to have `4-c=-5` and adding `c+5` on each side we get

`4-c+c+5=-5+c+5` i.e. `4-cancelc+cancelc+5=-cancel5+c+cancel5` or `9=c`.

Hence, `a=8`, `b=0` and `c=9`

(b) Here we have multiplication of a matrix `((3,1,10),(0,-5,4),(-2,2,-1))` by `ula` to get `((-9,-3,-30),(0,15,-12),(6,-6,3))`

In such cases each number in matrix is multiplied by `ula`.

For example for first element in first row we should have `axx3=-9`

Hence, `a=-9/3=-3`.

You can check for other elements too as each element is multiplied by `a=-3` to get the resultant matrix.