Multiply the Matrices [[6],[-9]][[9,-10]]

Problem

[[6],[−9]]*[[9,−10]]

Solution

1. Identify the dimensions of the matrices. The first matrix is a 2×1 column vector and the second matrix is a 1×2 row vector.

2. Determine the resulting matrix size. Multiplying a 2×1 matrix by a 1×2 matrix results in a 2×2 matrix.

3. Calculate each element (c_i*j) by multiplying the ith row of the first matrix by the jth column of the second matrix.

4. Compute the first row:

(c_11)=6⋅9=54

(c_12)=6⋅(−10)=−60

5. Compute the second row:

(c_21)=−9⋅9=−81

(c_22)=−9⋅(−10)=90

6. Assemble the final matrix using the calculated values.

Final Answer

[[6],[−9]]*[[9,−10]]=[[54,−60],[−81,90]]

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