a = [[1, 0, 3], [2, 1, - 1], [1, - 1, 1]] find a^2

To find \( A^2 \), where \( A \) is the matrix given by:

\[
A = \begin{bmatrix} 1 & 0 & 3 \\ 2 & 1 & -1 \\ 1 & -1 & 1 \end{bmatrix},
\]

we need to multiply the matrix \( A \) by itself:

\[
A^2 = A \times A.
\]

Let's perform the matrix multiplication:

\[
A^2 = \begin{bmatrix} 1 & 0 & 3 \\ 2 & 1 & -1 \\ 1 & -1 & 1 \end{bmatrix} \times \begin{bmatrix} 1 & 0 & 3 \\ 2 & 1 & -1 \\ 1 & -1 & 1 \end{bmatrix}.
\]

We'll compute this multiplication step-by-step:

The element at position \((i, j)\) in the resulting matrix is calculated as the dot product of the \(i\)-th row of the first matrix with the \(j\)-th column of the second matrix.

Let me calculate it for you.The result of \( A^2 \) is:

\[
A^2 = \begin{bmatrix} 4 & -3 & 6 \\ 3 & 2 & 4 \\ 0 & -2 & 5 \end{bmatrix}.
\]

Would you like any further details or have any questions?

Here are some related questions you might find interesting:

1. How do you find the inverse of a matrix?
2. What are the eigenvalues of matrix \( A \)?
3. How do you calculate the determinant of a matrix?
4. What does it mean for a matrix to be symmetric?
5. How can you determine if a matrix is diagonalizable?

**Tip:** When multiplying matrices, ensure the number of columns in the first matrix matches the number of rows in the second matrix for the multiplication to be valid.

a = [[1, 0, 3], [2, 1, -1], [1, -1, 1]] find a^2

Learn how to square a 3x3 matrix with a detailed step-by-step solution. This problem covers key concepts in linear algebra, including matrix multiplication and the related formula. Suitable for students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation