Multiply the Matrices

Problem

[[1,0,0],[0,1,0],[0,0,1]]*[[7],[11],[15]]

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 each element of the resulting vector is the dot product of a row from the first matrix and the column vector.

3. Calculate the first entry:

(1×7)+(0×11)+(0×15)=7

4. Calculate the second entry:

(0×7)+(1×11)+(0×15)=11

5. Calculate the third entry:

(0×7)+(0×11)+(1×15)=15

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]]*[[7],[11],[15]]=[[7],[11],[15]]

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