Multiply the Matrices [[a,b,c],[d,e,f],[g,h,i]][[1],[0],[0]]

Problem

[[a,b,c],[d,e,ƒ],[g,h,i]]*[[1],[0],[0]]

Solution

1. Identify the dimensions of the matrices. The first matrix is a 3×3 matrix and the second is a 3×1 column vector, resulting in a 3×1 matrix.

2. Apply the rule for matrix multiplication by multiplying each row of the first matrix by the column of the second matrix.

3. Calculate the first element of the resulting vector by taking the dot product of the first row and the column: a(1)+b(0)+c(0)

4. Calculate the second element by taking the dot product of the second row and the column: d(1)+e(0)+ƒ(0)

5. Calculate the third element by taking the dot product of the third row and the column: g(1)+h(0)+i(0)

6. Simplify the resulting expressions to find the final vector.

Final Answer

[[a,b,c],[d,e,ƒ],[g,h,i]]*[[1],[0],[0]]=[[a],[d],[g]]

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