Multiply the Matrices [[17,21,9]][[1,4,-3],[2,-1,2],[2,3,-4]]

Problem

[[17,21,9]]*[[1,4,−3],[2,−1,2],[2,3,−4]]

Solution

1. Identify the dimensions of the matrices. The first matrix is a 1×3 row vector and the second is a 3×3 square matrix. The resulting matrix will be a 1×3 row vector.

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

17*(1)+21*(2)+9*(2)=17+42+18=77

3. Calculate the second element of the product by multiplying the row by the second column of the second matrix.

17*(4)+21*(−1)+9*(3)=68−21+27=74

4. Calculate the third element of the product by multiplying the row by the third column of the second matrix.

17*(−3)+21*(2)+9*(−4)=−51+42−36=−45

5. Combine the results into a new 1×3 matrix.

Final Answer

[[17,21,9]]*[[1,4,−3],[2,−1,2],[2,3,−4]]=[[77,74,−45]]

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