Find the Variables

Problem

A=[[2,3,4],[2,3,1],[1,2,4]]*[[2,3,4],[2,3,1],[1,2,4]]

Solution

1. Identify the operation as matrix multiplication of a 3×3 matrix by itself.

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

(c_11)=(2)*(2)+(3)*(2)+(4)*(1)=4+6+4=14

(c_12)=(2)*(3)+(3)*(3)+(4)*(2)=6+9+8=23

(c_13)=(2)*(4)+(3)*(1)+(4)*(4)=8+3+16=27

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

(c_21)=(2)*(2)+(3)*(2)+(1)*(1)=4+6+1=11

(c_22)=(2)*(3)+(3)*(3)+(1)*(2)=6+9+2=17

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

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

(c_31)=(1)*(2)+(2)*(2)+(4)*(1)=2+4+4=10

(c_32)=(1)*(3)+(2)*(3)+(4)*(2)=3+6+8=17

(c_33)=(1)*(4)+(2)*(1)+(4)*(4)=4+2+16=22

5. Assemble the calculated values into the final matrix A

Final Answer

A=[[14,23,27],[11,17,15],[10,17,22]]

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