Multiply the Matrices [[7,3,2],[-4,3,5],[6,1,-1]]

Problem

[[7,3,2],[−4,3,5],[6,1,−1]]*[[7,3,2],[−4,3,5],[6,1,−1]]

Solution

1. Identify the operation as squaring the given 3×3 matrix by multiplying it by itself.

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)=(7)*(7)+(3)*(−4)+(2)*(6)=49−12+12=49

(c_12)=(7)*(3)+(3)*(3)+(2)*(1)=21+9+2=32

(c_13)=(7)*(2)+(3)*(5)+(2)*(−1)=14+15−2=27

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)=(−4)*(7)+(3)*(−4)+(5)*(6)=−28−12+30=−10

(c_22)=(−4)*(3)+(3)*(3)+(5)*(1)=−12+9+5=2

(c_23)=(−4)*(2)+(3)*(5)+(5)*(−1)=−8+15−5=2

4. Calculate the third row of the product by taking the dot product of the third row of the left matrix with each column of the right matrix.

(c_31)=(6)*(7)+(1)*(−4)+(−1)*(6)=42−4−6=32

(c_32)=(6)*(3)+(1)*(3)+(−1)*(1)=18+3−1=20

(c_33)=(6)*(2)+(1)*(5)+(−1)*(−1)=12+5+1=18

Final Answer

[[7,3,2],[−4,3,5],[6,1,−1]]*[[7,3,2],[−4,3,5],[6,1,−1]]=[[49,32,27],[−10,2,2],[32,20,18]]

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