Precalculus Unit 3 Test Review

Front

What is a matrix?

Back

A matrix is a rectangular array of numbers arranged in rows and columns.

Front

How do you determine the dimensions of a matrix?

Back

The dimensions of a matrix are given by the number of rows and columns it has, expressed as 'rows x 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

What is the result of multiplying two matrices?

Back

The result of multiplying two matrices is a new matrix where each element is the dot product of the corresponding row and column.

Front

What does it mean if two matrices are not compatible for multiplication?

Back

Two matrices are not compatible for multiplication if the number of columns in the first matrix does not equal the number of rows in the second matrix.

Front

What is the identity matrix?

Back

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

Front

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

Back

For a 2x2 matrix [[a, b], [c, d]], the inverse is (1/det) * [[d, -b], [-c, a]], where det = ad - bc.

Front

What is a scalar in matrix operations?

Back

A scalar is a single number that can multiply a matrix, affecting each element of the matrix.

Front

What is the process of row reduction?

Back

Row reduction is a method used to simplify a matrix to its row echelon form or reduced row echelon form using elementary row operations.

Front

What is a linear combination of vectors?

Back

A linear combination of vectors is a sum of scalar multiples of those vectors.