Multiply the Matrices

Problem

[[1,2,3*y],[4*z,7*x+y,y+2*x]]*[[7,6],[5,4],[3,2]]

Solution

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

2. Calculate the element in the first row, first column by taking the dot product of the first row of the left matrix and the first column of the right matrix.

(1)*(7)+(2)*(5)+(3*y)*(3)=7+10+9*y=17+9*y

3. Calculate the element in the first row, second column by taking the dot product of the first row of the left matrix and the second column of the right matrix.

(1)*(6)+(2)*(4)+(3*y)*(2)=6+8+6*y=14+6*y

4. Calculate the element in the second row, first column by taking the dot product of the second row of the left matrix and the first column of the right matrix.

(4*z)*(7)+(7*x+y)*(5)+(y+2*x)*(3)=28*z+35*x+5*y+3*y+6*x=41*x+8*y+28*z

5. Calculate the element in the second row, second column by taking the dot product of the second row of the left matrix and the second column of the right matrix.

(4*z)*(6)+(7*x+y)*(4)+(y+2*x)*(2)=24*z+28*x+4*y+2*y+4*x=32*x+6*y+24*z

6. Assemble the resulting matrix using the calculated components.

Final Answer

[[1,2,3*y],[4*z,7*x+y,y+2*x]]*[[7,6],[5,4],[3,2]]=[[17+9*y,14+6*y],[41*x+8*y+28*z,32*x+6*y+24*z]]

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