Determinants and Inverses of Matrices

Front

What is the inverse of a matrix?

Back

The inverse of a matrix A is another matrix, denoted A⁻¹, such that when A is multiplied by A⁻¹, the result is the identity matrix I. Not all matrices have inverses.

Tags

CCSS.HSA.REI.C.9

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 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 the identity matrix?

Back

The identity matrix is a square matrix with ones on the diagonal and zeros elsewhere. For a 2x2 matrix, it is ⌈1 & 0⌉
⌊0 & 1⌋.

Tags

CCSS.HSN.VM.C.10

Front

What must be true in order to add two matrices?

Back

The dimensions of the two matrices must be equal.

Tags

CCSS.HSN.VM.C.8

Front

What is the result of adding two matrices A and B?

Back

The result is a new matrix where each element is the sum of the corresponding elements of A and B.

Tags

CCSS.HSN.VM.C.8

Front

What is the product of two matrices?

Back

The product of two matrices A and B is a new matrix C, where each element C[i][j] is the sum of the products of the elements of the i-th row of A and the j-th column of B.

Tags

CCSS.HSN.VM.C.8

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 find the inverse of a 2x2 matrix?

Back

For a 2x2 matrix ⌈a & b⌉
⌊c & d⌋, the inverse is given by (1/det) * ⌈d & -b⌉
⌊-c & a⌋, where det = ad - bc.

Tags

CCSS.HSA.REI.C.9

Front

What is the determinant of the matrix ⌈4 & -3⌉
⌊12 & 3⌋?

Back

The determinant is calculated as (4)(3) - (-3)(12) = 12 + 36 = 48.