Find the following matrix​ product, if it exists.
left bracket Start 3 By 3 Matrix 1st Row 1st Column 1 2nd Column 0 3rd Column 0 2nd Row 1st Column 0 2nd Column 1 3rd Column 0 3rd Row 1st Column 0 2nd Column 0 3rd Column 1 EndMatrix right bracket 1	0	0	0	1	0	0	0	1  left bracket Start 3 By 3 Matrix 1st Row 1st Column negative 3 2nd Column 5 3rd Column negative 9 2nd Row 1st Column negative 5 2nd Column negative 8 3rd Column negative 7 3rd Row 1st Column 0 2nd Column negative 1 3rd Column 2 EndMatrix right bracket −3	5	−9	−5	−8	−7	0	−1	2 

The given problem involves the multiplication of two \( 3 \times 3 \) matrices. Let's denote the two matrices as:

\[
A = \begin{pmatrix}
1 & 0 & 0 \\
0 & 1 & 0 \\
0 & 0 & 1
\end{pmatrix}
\]
and
\[
B = \begin{pmatrix}
-3 & 5 & -9 \\
-5 & -8 & -7 \\
0 & -1 & 2
\end{pmatrix}.
\]

### Step 1: Understand Matrix Multiplication
Matrix multiplication is done by taking the dot product of the rows of the first matrix with the columns of the second matrix.

### Step 2: Perform the Multiplication
Since \( A \) is the identity matrix, the multiplication of \( A \) with any matrix \( B \) will yield \( B \) itself. This is because the identity matrix has no effect on the result when multiplying it with any matrix.

\[
A \cdot B = B = \begin{pmatrix}
-3 & 5

Find the following matrix product, if it exists: 
Matrix A: 
1 0 0 
0 1 0 
0 0 1 
Matrix B: 
-3 5 -9 
-5 -8 -7 
0 -1 2

Discover how to find the matrix product of a 3x3 identity matrix and another 3x3 matrix. This problem demonstrates key concepts in matrix multiplication and identity matrix properties, suitable for students in Grades 11-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation