Find the Variables

Problem

[[a,b,c],[d,e,ƒ],[g,h,i]]*[[−3,−3,−2],[1,−5,5],[−3,−1,3]]=[[−3,−1,3],[1,−5,5],[−3,−3,−2]]

Solution

1. Identify the relationship between the rows of the product matrix and the rows of the second matrix on the left-hand side.

2. Observe that the first row of the product, [−3,−1,3] is identical to the third row of the second matrix.

3. Observe that the second row of the product, [1,−5,5] is identical to the second row of the second matrix.

4. Observe that the third row of the product, [−3,−3,−2] is identical to the first row of the second matrix.

5. Recall that multiplying a matrix M by a matrix A on the left (A*M results in a linear combination of the rows of M

6. Determine the coefficients for the first row of A to produce the third row of M a=0,b=0,c=1

7. Determine the coefficients for the second row of A to produce the second row of M d=0,e=1,ƒ=0

8. Determine the coefficients for the third row of A to produce the first row of M g=1,h=0,i=0

Final Answer

[[a,b,c],[d,e,ƒ],[g,h,i]]=[[0,0,1],[0,1,0],[1,0,0]]

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