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  3. ZuAI AP College Board Pre-Calculus
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The Inverse and Determinant of a Matrix

Henry Lee

Henry Lee

7 min read

Next Topic - Linear Transformations and Matrices
Study Guide Overview

This study guide covers matrices, focusing on inverses and determinants. It explains the identity matrix, 2x2 inverse formula, and how to calculate 2x2 and 3x3 determinants. It also explores the relationship between determinants and parallel vectors and the condition for a matrix to be invertible (det(A) ≠ 0). Finally, it includes practice questions and exam tips.

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Previous Topic - MatricesNext Topic - Linear Transformations and Matrices

Question 1 of 11

Which of the following is a 3x3 identity matrix? 🤔

[100010001]\begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{bmatrix}​100​010​001​​

[010100001]\begin{bmatrix} 0 & 1 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & 1 \end{bmatrix}​010​100​001​​

[111111111]\begin{bmatrix} 1 & 1 & 1 \\ 1 & 1 & 1 \\ 1 & 1 & 1 \end{bmatrix}​111​111​111​​

[101010101]\begin{bmatrix} 1 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 1 \end{bmatrix}​101​010​101​​