Multiply the Matrices [[0,-2],[2,3]][[-4,1,4],[-6,4,-6]]

Problem

[[0,−2],[2,3]]*[[−4,1,4],[−6,4,−6]]

Solution

1. Identify the dimensions of the matrices to ensure they can be multiplied. The first matrix is 2×2 and the second is 2×3 so the resulting matrix will be 2×3

2. Calculate the first row of the product by taking the dot product of the first row of the left matrix with each column of the right matrix.

(c_11)=(0)*(−4)+(−2)*(−6)=12

(c_12)=(0)*(1)+(−2)*(4)=−8

(c_13)=(0)*(4)+(−2)*(−6)=12

3. Calculate the second row of the product by taking the dot product of the second row of the left matrix with each column of the right matrix.

(c_21)=(2)*(−4)+(3)*(−6)=−8−18=−26

(c_22)=(2)*(1)+(3)*(4)=2+12=14

(c_23)=(2)*(4)+(3)*(−6)=8−18=−10

4. Assemble the calculated values into the final 2×3 matrix.

Final Answer

[[0,−2],[2,3]]*[[−4,1,4],[−6,4,−6]]=[[12,−8,12],[−26,14,−10]]

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