Practice Algebra 2 2x2 Matrices, Determinants, and Inverses

Front

What are the dimensions of the product of two matrices A (3x2) and B (2x3)?

Back

3 X 3

Front

What is the first step to find the inverse of a 2x2 matrix?

Back

Calculate the determinant of the matrix.

Front

What is the formula for the determinant of a 2x2 matrix |A| = |a b; c d|?

Back

|A| = ad - bc.

Front

What does it mean if the determinant of a matrix is 0?

Back

The matrix is singular and does not have an inverse.

Front

How do you calculate the determinant of a 3x3 matrix?

Back

Use the rule of Sarrus or cofactor expansion.

Front

What is the determinant of the matrix |1 2 3; 4 5 6; 7 8 9|?

Back

0

Front

What is the inverse of a 2x2 matrix |a b; c d|?

Back

(1/det(A)) * |d -b; -c a| if det(A) ≠ 0.

Front

What is the determinant of the matrix |2 3; 5 7|?

Back

(2*7) - (3*5) = 14 - 15 = -1.

Front

What is the relationship between a matrix and its inverse?

Back

A matrix A multiplied by its inverse A⁻¹ equals the identity matrix I.

Front

What is the identity matrix for 2x2 matrices?

Back

|1 0; 0 1|.