Multiply the Matrices

Problem

[[2,0,−5],[0,−3,7],[0,0,1]]*[[11],[8],[4]]

Solution

1. Identify the dimensions of the matrices. The first matrix is 3×3 and the second is 3×1 so the resulting matrix will be 3×1

2. Calculate the first entry by multiplying the first row of the left matrix by the column vector.

2*(11)+0*(8)+(−5)*(4)=22+0−20=2

3. Calculate the second entry by multiplying the second row of the left matrix by the column vector.

0*(11)+(−3)*(8)+7*(4)=0−24+28=4

4. Calculate the third entry by multiplying the third row of the left matrix by the column vector.

0*(11)+0*(8)+1*(4)=0+0+4=4

5. Assemble the results into the final 3×1 matrix.

Final Answer

[[2,0,−5],[0,−3,7],[0,0,1]]*[[11],[8],[4]]=[[2],[4],[4]]

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