https://file.aiquickdraw.com/mathbot/file/17272051561341p7uugym.jpg

The image shows a matrix-related multiple-choice question. The matrix given is:

\[
A = \begin{pmatrix}
1 & 0 & 0 \\
0 & 1 & 0 \\
0 & 0 & 1
\end{pmatrix}
\]

This is a 3x3 identity matrix.

The identity matrix \( I_3 \) has the following properties:

1. **Determinant**: The determinant of an identity matrix is always 1.
2. **Inverse**: The inverse of an identity matrix is itself.
3. **Eigenvalues**: All eigenvalues of an identity matrix are 1.
4. **Symmetric**: An identity matrix is symmetric, meaning \( A = A^T \).
5. **Diagonal**: It is a diagonal matrix because all off-diagonal elements are zero.

The question asks, "Which of the following is *not* true about the matrix \( A \)?"

While the full list of answer choices is not shown, based on the properties above, a correct answer would involve a statement that contradicts any of the properties above. For example, an incorrect statement might claim that the determinant is not 1, or that the matrix has a different inverse or eigenvalues.

Would you like more details on specific matrix properties, or can I help you further with this question?

### Related Questions:
1. What are the properties of a diagonal matrix?
2. How do you calculate the determinant of a 3x3 matrix?
3. What is the significance of eigenvalues for a matrix?
4. What does it mean for a matrix to be orthogonal?
5. How can we verify if a matrix is invertible?

### Tip:
The identity matrix is a fundamental matrix in linear algebra because it acts as the neutral element in matrix multiplication, i.e., \( A \cdot I = A \).

Which of the following is not true about the matrix A = (1 0 0; 0 1 0; 0 0 1)?

Learn how to analyze the properties of the 3x3 identity matrix. Understand its determinant, inverse, eigenvalues, and symmetry, while identifying which statements about it are true or false. Suitable for high school students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation