AMDM 1 Unit 5 Test

Front

What is matrix multiplication?

Back

Matrix multiplication is a binary operation that produces a matrix from two matrices. The number of columns in the first matrix must equal the number of rows in the second matrix.

Front

How do you find the product of two matrices?

Back

To find the product of two matrices, multiply the rows of the first matrix by the columns of the second matrix and sum the products.

Front

What is a determinant of a matrix?

Back

The determinant is a scalar value that is a function of the entries of a square matrix. It provides important information about the matrix, including whether it is invertible.

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 does it mean for two matrices to be inverses of each other?

Back

Two matrices A and B are inverses if their product is the identity matrix, i.e., AB = I and BA = I.

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 condition for matrix multiplication to be defined?

Back

Matrix multiplication is defined when the number of columns in the first matrix equals the number of rows in the second matrix.

Front

What is a square matrix?

Back

A square matrix is a matrix with the same number of rows and columns.

Front

What is the product of the matrices [[1, 2], [3, 4]] and [[5, 6], [7, 8]]?

Back

The product is [[19, 22], [43, 50]].

Front

What is the result of multiplying a matrix by the zero matrix?

Back

The result of multiplying any matrix by the zero matrix is the zero matrix.