Matrix Test Review

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.

Front

How do you find 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 matrix subtraction?

Back

Matrix subtraction involves subtracting corresponding elements of two matrices of the same dimensions.

Front

How do you perform scalar multiplication on a matrix?

Back

Scalar multiplication involves multiplying each element of a matrix by a scalar (a constant number).

Front

What is a scalar matrix?

Back

A scalar matrix is a square matrix in which all the elements are equal to the same scalar value.

Front

What is the identity matrix?

Back

The identity matrix is a square matrix with ones on the diagonal and zeros elsewhere. It acts as the multiplicative identity in matrix multiplication.

Front

What is the relationship between a matrix and its inverse?

Back

If A is a matrix and A⁻¹ is its inverse, then A * A⁻¹ = I, where I is the identity matrix.

Front

What does it mean for a matrix to be singular?

Back

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

Front

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

Back

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

Front

What is the transpose of a matrix?

Back

The transpose of a matrix is obtained by flipping it over its diagonal, turning rows into columns and vice versa.