Matrix Multiplication Warm Up

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.

Tags

CCSS.HSN.VM.C.8

Front

What are the dimensions of a product of two matrices?

Back

If matrix A is of dimension m x n and matrix B is of dimension n x p, then the product AB will have dimensions m x p.

Tags

CCSS.HSN.VM.C.8

Front

How do you multiply two matrices?

Back

To multiply two matrices, take the dot product of the rows of the first matrix with the columns of the second matrix.

Tags

CCSS.HSN.VM.C.8

Front

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

Back

Multiplying any matrix by the identity matrix of appropriate size leaves the original matrix unchanged.

Tags

CCSS.HSN.VM.C.10

Front

What is the zero matrix?

Back

The zero matrix is a matrix in which all elements are zero. It acts as the additive identity in matrix addition.

Front

What is the transpose of a matrix?

Back

The transpose of a matrix is obtained by swapping its rows and columns.

Front

What is the determinant of a matrix?

Back

The determinant is a scalar value that can be computed from the elements of a square matrix and provides important properties of the matrix.

Front

What is a scalar multiplication of a matrix?

Back

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

Tags

CCSS.HSN.VM.C.7

Front

What is the associative property of matrix multiplication?

Back

The associative property states that (AB)C = A(BC) for any matrices A, B, and C where the products are defined.

Tags

CCSS.HSN.VM.C.9

Front

What is the distributive property of matrix multiplication?

Back

The distributive property states that A(B + C) = AB + AC for any matrices A, B, and C where the products are defined.

Tags

CCSS.HSN.VM.C.9