Matrices

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 dot product of two vectors?

Back

The dot product is a scalar value obtained by multiplying corresponding entries of two sequences of numbers and summing those products.

Front

How do you multiply two matrices?

Back

To multiply two matrices, the number of columns in the first matrix must equal the number of rows in the second matrix. The entry in the resulting matrix is obtained by taking the dot product of the corresponding row and column.

Tags

CCSS.HSN.VM.C.8

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.

Tags

CCSS.HSN.VM.C.10

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.

Tags

CCSS.HSA.REI.C.9

Front

What does it mean for matrices to be compatible for addition?

Back

Two matrices are compatible for addition if they have the same dimensions (i.e., the same number of rows and columns).

Tags

CCSS.HSN.VM.C.8

Front

What is a determinant?

Back

The determinant is a scalar value that can be computed from the elements of a square matrix and provides important properties about the matrix, such as whether it is invertible.

Front

What is a zero matrix?

Back

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

Front

What is a transpose of a matrix?

Back

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

Front

What is a scalar multiplication of a matrix?

Back

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

Tags

CCSS.HSN.VM.C.7