If and are two square matrices, find A B and hence solve the system of linear equations: X – y = 3, 2x + 3y + 4z = 17, y + 2z = 7.(CBSE 2012)

Question

If and are two square matrices, find A B and hence solve the system of linear equations: X &ndash; y = 3, 2x + 3y + 4z = 17, y + 2z = 7.(CBSE 2012)

Philoid · Accepted Answer

A =  B = 
AB =

AB =

Now, we can see that it is AB = 6I. where I is the unit Matrix

Or, A &ndash; 1 =

Now the given equation can be written as:

A X B

Or, X = A &ndash; 1B

=

X =

Hence, x = 2,y = &ndash; 1 and z = 4