Multiply the Matrices -3[[1,3,5],[2,1,4]][[-5],[4],[-3]]

Problem

−3*[[1,3,5],[2,1,4]]*[[−5],[4],[−3]]

Solution

1. Multiply the two matrices first by calculating the dot product of each row of the first matrix with the column of the second matrix.

2. Calculate the first element of the resulting vector: (1)*(−5)+(3)*(4)+(5)*(−3)=−5+12−15=−8

3. Calculate the second element of the resulting vector: (2)*(−5)+(1)*(4)+(4)*(−3)=−10+4−12=−18

4. Apply the scalar multiplication by multiplying each element of the resulting vector by −3

5. Simplify the final vector: −3×−8=24 and −3×−18=54

Final Answer

−3*[[1,3,5],[2,1,4]]*[[−5],[4],[−3]]=[[24],[54]]

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