Multiply the Matrices [[8,9,0],[-1,-2,3]]*[[4],[5],[6]]

Problem

[[8,9,0],[−1,−2,3]]*[[4],[5],[6]]

Solution

1. Identify the dimensions of the matrices to ensure multiplication is possible. The first matrix is 2×3 and the second is 3×1 Since the number of columns in the first matches the number of rows in the second, the resulting matrix will be 2×1

2. Calculate the first element of the resulting matrix by taking the dot product of the first row of the first matrix and the column of the second matrix.

8*(4)+9*(5)+0*(6)

32+45+0=77

3. Calculate the second element of the resulting matrix by taking the dot product of the second row of the first matrix and the column of the second matrix.

−1*(4)+(−2)*(5)+3*(6)

−4−10+18=4

4. Construct the final 2×1 matrix using the calculated values.

Final Answer

[[8,9,0],[−1,−2,3]]*[[4],[5],[6]]=[[77],[4]]

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