Finding Determinant & Inverse of Matrices Flashcard

Front

What is the determinant of a 2x2 matrix?

Back

For a 2x2 matrix A = ⌈a b⌉
⌊c d⌋, the determinant is calculated as det(A) = ad - bc.

Front

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

Back

For a 3x3 matrix A = ⌈a b c⌉
⌊d e f⌋
⌊g h i⌋, the determinant is det(A) = a(ei - fh) - b(di - fg) + c(dh - eg).

Front

What is the inverse of a matrix?

Back

The inverse of a matrix A is another matrix A⁻¹ such that AA⁻¹ = I, where I is the identity matrix.

Tags

CCSS.HSA.REI.C.9

Front

What is the formula for finding the inverse of a 2x2 matrix?

Back

For a 2x2 matrix A = ⌈a b⌉
⌊c d⌋, the inverse is A⁻¹ = (1/det(A)) * ⌈d -b⌉
⌊-c a⌋, provided det(A) ≠ 0.

Tags

CCSS.HSA.REI.C.9

Front

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

Back

If det(A) = 0, the matrix A is singular, meaning it does not have an inverse.

Tags

CCSS.HSA.REI.C.9

Front

Calculate the determinant of the matrix ⌈3 0⌉
⌊0 2⌋.

Back

det(A) = 3*2 - 0*0 = 6.

Front

What is the determinant of the identity matrix?

Back

The determinant of the identity matrix I is 1.

Front

How do you find the determinant of a triangular matrix?

Back

For a triangular matrix, the determinant is the product of the diagonal elements.

Front

What is the relationship between the determinant and the area of a parallelogram?

Back

The absolute value of the determinant of a 2x2 matrix represents the area of the parallelogram formed by its column vectors.

Front

What is the effect of row operations on the determinant?

Back

1. Swapping two rows multiplies the determinant by -1.
2. Multiplying a row by a scalar multiplies the determinant by that scalar.
3. Adding a multiple of one row to another does not change the determinant.