Question - Matrix Multiplication with Identity Matrix
Solution:
The image shows a matrix equation where matrix A is given, and we need to calculate the product of matrix A with another matrix.Matrix A is:\[ A = \begin{bmatrix}3 & -5 & 6 \\-2 & 4 & 2 \\-1 & 0 & 3\end{bmatrix} \]And it needs to be multiplied by the matrix:\[ \begin{bmatrix}1 & 0 & 0 \\0 & 1 & 0 \\0 & 0 & 1\end{bmatrix} \]This second matrix is the identity matrix $$ I_3 $$ of size 3x3. The matrix product of any matrix with the identity matrix of the appropriate size is the original matrix itself. That's because the identity matrix acts like the number 1 for matrix multiplication.Therefore, the product of matrix A with this identity matrix is matrix A unchanged:\[ A \cdot I_3 = \begin{bmatrix}3 & -5 & 6 \\-2 & 4 & 2 \\-1 & 0 & 3\end{bmatrix} \]
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