Find the Inverse of the Resulting Matrix

Problem

[[a,b,d]]*[[1,5,0],[5,3,6],[0,6,2]]*[[a],[b],[d]]

Solution

1. Multiply the row vector by the 3×3 matrix.

[[a,b,d]]*[[1,5,0],[5,3,6],[0,6,2]]=[[a+5*b,5*a+3*b+6*d,6*b+2*d]]

2. Multiply the resulting row vector by the column vector.

[[a+5*b,5*a+3*b+6*d,6*b+2*d]]*[[a],[b],[d]]=a*(a+5*b)+b*(5*a+3*b+6*d)+d*(6*b+2*d)

3. Expand the algebraic expression.

a2+5*a*b+5*a*b+3*b2+6*b*d+6*b*d+2*d2

4. Combine like terms to find the resulting scalar value.

a2+10*a*b+3*b2+12*b*d+2*d2

5. Find the inverse of the resulting 1×1 matrix. The inverse of a scalar x is 1/x

(a2+10*a*b+3*b2+12*b*d+2*d2)(−1)=1/(a2+10*a*b+3*b2+12*b*d+2*d2)

Final Answer

([[a,b,d]]*[[1,5,0],[5,3,6],[0,6,2]]*[[a],[b],[d]])(−1)=1/(a2+10*a*b+3*b2+12*b*d+2*d2)

Want more problems? Check here!