Multiply the Matrices [[-4,x],[-8,4]][[-4,x],[-8,4]]

Problem

[[−4,x],[−8,4]]*[[−4,x],[−8,4]]

Solution

1. Identify the dimensions of the matrices. Both are 2×2 matrices, so the resulting product will also be a 2×2 matrix.

2. Calculate the element in the first row, first column by multiplying the first row of the first matrix by the first column of the second matrix.

(−4)*(−4)+(x)*(−8)=16−8*x

3. Calculate the element in the first row, second column by multiplying the first row of the first matrix by the second column of the second matrix.

(−4)*(x)+(x)*(4)=−4*x+4*x=0

4. Calculate the element in the second row, first column by multiplying the second row of the first matrix by the first column of the second matrix.

(−8)*(−4)+(4)*(−8)=32−32=0

5. Calculate the element in the second row, second column by multiplying the second row of the first matrix by the second column of the second matrix.

(−8)*(x)+(4)*(4)=−8*x+16

6. Combine the results into the final matrix structure.

Final Answer

[[−4,x],[−8,4]]*[[−4,x],[−8,4]]=[[16−8*x,0],[0,16−8*x]]

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