How do you find the values of x, y and z given #3[(x, y-1), (4, 3z)]=[(15, 6), (6z, 3x+y)]#?
First step is to multiply the matrix on the left by
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.
From the first three equations we can calculate the values of each variable:
#3x=15 => x=5#
#3y-3=6 => 3y=9 => y=3#
#6z=12 => z=2#
Now we have to check if the calculated values fulfill the last equation:
Left side equals right side, so the calculated values are solutions to all 4 equations.
Answer: The equation is true for