Determinants and Inverses of Matrices

Front

What is a determinant of a matrix?

Back

A determinant is a scalar value that is a function of the entries of a square matrix. It provides important information about the matrix, such as whether it is invertible.

Front

How do you calculate the determinant of a 2x2 matrix?

Back

For a 2x2 matrix [[a, b], [c, d]], the determinant is calculated as ad - bc.

Front

What is the determinant of the matrix [[3, 2], [1, 4]]?

Back

The determinant is (3*4) - (2*1) = 12 - 2 = 10.

Front

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

Back

If the determinant is zero, the matrix is singular, meaning it does not have an inverse and the system of equations it represents does not have a unique solution.

Tags

CCSS.HSA.REI.C.9

Front

What is the formula for the determinant of a 3x3 matrix?

Back

For a 3x3 matrix [[a, b, c], [d, e, f], [g, h, i]], the determinant is a(ei - fh) - b(di - fg) + c(dh - eg).

Front

How do you find the inverse of a matrix?

Back

To find the inverse of a matrix A, you can use the formula A^(-1) = (1/det(A)) * adj(A), where adj(A) is the adjugate of A.

Tags

CCSS.HSA.REI.C.9

Front

What is the adjugate of a matrix?

Back

The adjugate of a matrix is the transpose of the cofactor matrix. It is used in calculating the inverse of a matrix.

Front

What is the condition for a matrix to have an inverse?

Back

A matrix has an inverse if and only if its determinant is non-zero.

Tags

CCSS.HSA.REI.C.9

Front

What is a singular matrix?

Back

A singular matrix is a square matrix that does not have an inverse, which occurs when its determinant is zero.

Tags

CCSS.HSA.REI.C.9

Front

How do you determine if a system of equations has a unique solution using determinants?

Back

If the determinant of the coefficient matrix is non-zero, the system has a unique solution.

Tags

CCSS.HSA.REI.C.9