Math Problem Statement

Find A² where A = [[2, -1, 1], [2, -1, 0], [1, 0, 0]].

Solution

numpy as np

Define the matrix A

A = np.array([[2, -1, 1], [2, -1, 0], [1, 0, 0]])

Calculate A^2

A_squared = np.dot(A, A) A_squaredThe square of matrix AA (A2A^2) is:

\begin{bmatrix} 3 & -1 & 2 \\ 2 & -1 & 2 \\ 2 & -1 & 1 \end{bmatrix}$$ Let me know if you want a detailed explanation of the steps or have other questions! ### Related Questions: 1. How is matrix multiplication performed step-by-step? 2. What is the significance of squaring a matrix in linear algebra? 3. How can I compute higher powers of a matrix ($$A^3, A^4, \dots$$)? 4. Are there any shortcuts for calculating powers of diagonalizable matrices? 5. Can $$A^2$$ be used to find eigenvalues or

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Math Problem Analysis

Mathematical Concepts

Matrix Multiplication
Linear Algebra

Formulas

Matrix multiplication formula: C[i][j] = Σ(A[i][k] * B[k][j]) for all k.

Theorems

Associativity of matrix multiplication.

Suitable Grade Level

Grades 11-12 or College Level