Question

How do you find the values of x, y and z given `3[(x, y-1), (4, 3z)]=[(15, 6), (6z, 3x+y)]`?

Answer 1

See explanation.

Explanation:

First step is to multiply the matrix on the left by `3` (to multiply a matrix by a number you have to multiply a;; elements of the matrix by the number):

`3xx[(x,y-1),(4,3z)]=[(15,6),(6z,3x+y)]`

`[(3x,3y-3),(12,9z)]=[(15,6),(6z,3x+y)]`

To check when 2 square matrices are equal we have to check if all their elements are equal.

So in this example we get such set of equations.

`{(3x=15),(3y-3=6),(6z=12),(9z=3x+y):}`

From the first three equations we can calculate the values of each variable:

1. `3x=15 => x=5`

2. `3y-3=6 => 3y=9 => y=3`

3. `6z=12 => z=2`

Now we have to check if the calculated values fulfill the last equation:

`9*2=3*5+3`

`18=18`

Left side equals right side, so the calculated values are solutions to all 4 equations.

Answer: The equation is true for `x=5,y=3,z=2`