Multiply the Matrices

Problem

[[−1/19,−2/19,−14/95],[−13/95,−7/95,−11/475],[−3/95,13/95,34/475]]*[[1,0,0],[0,1,0],[0,4,1]]

Solution

1. Identify the dimensions of the matrices. Both are 3×3 matrices, so the resulting matrix will also be 3×3

2. Calculate the first column of the product. Since the first column of the second matrix is [1,0,0]T the first column of the result is simply the first column of the first matrix.

(c_11)=−1/19*(1)+−2/19*(0)+−14/95*(0)=−1/19

(c_21)=−13/95*(1)+−7/95*(0)+−11/475*(0)=−13/95

(c_31)=−3/95*(1)+13/95*(0)+34/475*(0)=−3/95

3. Calculate the second column of the product. Multiply each row of the first matrix by the second column of the second matrix [0,1,4]T

(c_12)=−1/19*(0)+−2/19*(1)+−14/95*(4)=−2/19−56/95=−10/95−56/95=−66/95

(c_22)=−13/95*(0)+−7/95*(1)+−11/475*(4)=−7/95−44/475=−35/475−44/475=−79/475

(c_32)=−3/95*(0)+13/95*(1)+34/475*(4)=13/95+136/475=65/475+136/475=201/475

4. Calculate the third column of the product. Since the third column of the second matrix is [0,0,1]T the third column of the result is the third column of the first matrix.

(c_13)=−1/19*(0)+−2/19*(0)+−14/95*(1)=−14/95

(c_23)=−13/95*(0)+−7/95*(0)+−11/475*(1)=−11/475

(c_33)=−3/95*(0)+13/95*(0)+34/475*(1)=34/475

Final Answer

[[−1/19,−2/19,−14/95],[−13/95,−7/95,−11/475],[−3/95,13/95,34/475]]*[[1,0,0],[0,1,0],[0,4,1]]=[[−1/19,−66/95,−14/95],[−13/95,−79/475,−11/475],[−3/95,201/475,34/475]]

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