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

1 Answer
Dec 1, 2016

Answer:

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#