Question

Find x1 and x2.

left bracket Start 2 By 2 Matrix 1st Row 1st Column negative 4 2nd Column 1 2nd Row 1st Column 5 2nd Column 4 End Matrix right bracket left bracket Start 2 By 1 Matrix 1st Row 1st Column x 1 2nd Row 1st Column x 2 End Matrix right bracket plus left bracket Start 2 By 1 Matrix 1st Row 1st Column 11 2nd Row 1st Column negative 19 EndMatrix right bracket equals left bracket Start 2 By 1 Matrix 1st Row 1st Column negative 11 2nd Row 1st Column 40 End Matrix right bracket

Answer 1

To find x₁ and x₂ :

Step 1:

Multiplying first 2 X 2 matrix with 2 X 1 vector, we get:

Step 2:
Adding the 2 X 1 matrices on LHS, we get:

Step 3:

Thus, we get:

and

Step 4:
Simplifying, we get:

                 (1)

and

                   (2)

Step 5:

4 X (1) gives:

          (3)

Step 6:

(2) - (3) gives:

So,

Substituting in (1), we get:

So,

we get:

So,

Answer is: