Matrices ACT Prep

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

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

Front

How do you find the inverse of a matrix?

Back

The inverse of a matrix A, denoted A^-1, is found such that AA^-1 = I, where I is the identity matrix. For a 2x2 matrix, A^-1 = (1/det(A)) * [[d, -b], [-c, a]].

Front

What does it mean for a matrix to be singular?

Back

A matrix is singular if its determinant is zero, meaning it does not have an inverse.

Front

What is matrix multiplication?

Back

Matrix multiplication involves multiplying rows of the first matrix by columns of the second matrix. The number of columns in the first matrix must equal the number of rows in the second.

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 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.

Front

How do you add two matrices?

Back

To add two matrices, they must be of the same dimensions. Add corresponding elements together.

Front

What is a scalar multiplication of a matrix?

Back

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

Front

What is a row echelon form?

Back

Row echelon form is a form of a matrix where all non-zero rows are above any rows of all zeros, and leading coefficients of non-zero rows are to the right of leading coefficients of the previous rows.