Matrices - Determinants and Inverses

Front

What is a matrix?

Back

A matrix is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns.

Front

What is the determinant of a 2x2 matrix?

Back

The determinant of a 2x2 matrix is calculated using the formula ad - bc, where the matrix is represented as [[a, b], [c, d]].

Front

What does it mean if a matrix has no inverse?

Back

A matrix has no inverse if its determinant is zero, indicating that it is singular and does not span the entire space.

Tags

CCSS.HSA.REI.C.9

Front

How do you find the inverse of a 2x2 matrix?

Back

To find the inverse of a 2x2 matrix [[a, b], [c, d]], use the formula (1/det) * [[d, -b], [-c, a]], where det = ad - bc.

Tags

CCSS.HSA.REI.C.9

Front

What is the size of a matrix?

Back

The size of a matrix is defined by the number of rows and columns it contains, expressed as 'rows x columns'.

Front

What is a singular matrix?

Back

A singular matrix is a square matrix that does not have an inverse, typically because its determinant is zero.

Tags

CCSS.HSA.REI.C.9

Front

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

Back

The determinant of a 3x3 matrix can be calculated using the rule of Sarrus or cofactor expansion.

Front

What is the relationship between a matrix and its inverse?

Back

A matrix A and its inverse A^-1 satisfy the equation A * A^-1 = I, where I is the identity matrix.

Tags

CCSS.HSA.REI.C.9

Front

What is an identity matrix?

Back

An identity matrix is a square matrix with ones on the diagonal and zeros elsewhere, denoted as I.

Tags

CCSS.HSN.VM.C.10

Front

How can you determine if a matrix is invertible?

Back

A matrix is invertible if its determinant is non-zero.

Tags

CCSS.HSA.REI.C.9