Multiply the Matrices [[1,0,0],[0,1,0],[0,0,1]]*[[3],[1],[-2]]

Problem

[[1,0,0],[0,1,0],[0,0,1]]*[[3],[1],[−2]]

Solution

1. Identify the matrices being multiplied. The first matrix is a 3×3 identity matrix, denoted as I and the second is a 3×1 column vector.

2. Apply the rule for matrix multiplication where the element in the ith row is the dot product of the ith row of the first matrix and the column of the second matrix.

3. Calculate the first entry:

(1)*(3)+(0)*(1)+(0)*(−2)=3

4. Calculate the second entry:

(0)*(3)+(1)*(1)+(0)*(−2)=1

5. Calculate the third entry:

(0)*(3)+(0)*(1)+(1)*(−2)=−2

6. Recognize that multiplying any matrix by the identity matrix I results in the original matrix.

Final Answer

[[1,0,0],[0,1,0],[0,0,1]]*[[3],[1],[−2]]=[[3],[1],[−2]]

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