Simplify the Matrix [[2,-5],[1,4]][[6,2,3],[-4,0,7]]

Problem

[[2,−5],[1,4]]*[[6,2,3],[−4,0,7]]

Solution

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

2. Calculate the elements of the first row by multiplying the first row of the left matrix by each column of the right matrix.

(c_11)=(2)*(6)+(−5)*(−4)=12+20=32

(c_12)=(2)*(2)+(−5)*(0)=4+0=4

(c_13)=(2)*(3)+(−5)*(7)=6−35=−29

3. Calculate the elements of the second row by multiplying the second row of the left matrix by each column of the right matrix.

(c_21)=(1)*(6)+(4)*(−4)=6−16=−10

(c_22)=(1)*(2)+(4)*(0)=2+0=2

(c_23)=(1)*(3)+(4)*(7)=3+28=31

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

Final Answer

[[2,−5],[1,4]]*[[6,2,3],[−4,0,7]]=[[32,4,−29],[−10,2,31]]

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