Multiply the Matrices

Problem

[[−9/170,29/170,−4/85],[−21/170,11/170,19/85],[1/10,−1/10,1/5]]*[[6],[−4],[0]]

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 element of the product by multiplying the first row of the first matrix by the column vector.

(R_1)=(−9/170)*(6)+(29/170)*(−4)+(−4/85)*(0)

(R_1)=−54/170−116/170+0

(R_1)=−170/170=−1

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

(R_2)=(−21/170)*(6)+(11/170)*(−4)+(19/85)*(0)

(R_2)=−126/170−44/170+0

(R_2)=−170/170=−1

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

(R_3)=(1/10)*(6)+(−1/10)*(−4)+(1/5)*(0)

(R_3)=6/10+4/10+0

(R_3)=10/10=1

Final Answer

[[−9/170,29/170,−4/85],[−21/170,11/170,19/85],[1/10,−1/10,1/5]]*[[6],[−4],[0]]=[[−1],[−1],[1]]

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