Add, Subtract and Scalar Multiply Matrices

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What is matrix addition?

Back

Matrix addition is the operation of adding two matrices by adding their corresponding elements. For two matrices A and B of the same dimensions, the sum C is defined as C[i][j] = A[i][j] + B[i][j].

Tags

CCSS.HSN.VM.C.8

Front

What is matrix subtraction?

Back

Matrix subtraction is the operation of subtracting one matrix from another by subtracting their corresponding elements. For two matrices A and B of the same dimensions, the difference C is defined as C[i][j] = A[i][j] - B[i][j].

Tags

CCSS.HSN.VM.C.8

Front

What is scalar multiplication of a matrix?

Back

Scalar multiplication of a matrix involves multiplying each element of the matrix by a scalar (a single number). If k is a scalar and A is a matrix, then the resulting matrix B is defined as B[i][j] = k * A[i][j].

Tags

CCSS.HSN.VM.C.7

Front

What are the conditions for matrix addition?

Back

Matrix addition can only be performed on matrices of the same dimensions. If A is an m x n matrix and B is also an m x n matrix, then A + B is defined.

Tags

CCSS.HSN.VM.C.8

Front

What are the conditions for matrix subtraction?

Back

Matrix subtraction can only be performed on matrices of the same dimensions. If A is an m x n matrix and B is also an m x n matrix, then A - B is defined.

Tags

CCSS.HSN.VM.C.8

Front

How do you perform scalar multiplication on a matrix?

Back

To perform scalar multiplication on a matrix, multiply each element of the matrix by the scalar. For example, if k is a scalar and A is a matrix, then the new matrix B is obtained by B[i][j] = k * A[i][j] for all elements.

Tags

CCSS.HSN.VM.C.7

Front

What is the result of adding a zero matrix to another matrix?

Back

Adding a zero matrix to another matrix does not change the original matrix. If A is any matrix and O is a zero matrix of the same dimensions, then A + O = A.

Front

What is the result of subtracting a matrix from itself?

Back

Subtracting a matrix from itself results in a zero matrix. If A is any matrix, then A - A = O, where O is a zero matrix of the same dimensions.

Tags

CCSS.HSN.VM.C.10

Front

Can you add or subtract matrices of different dimensions?

Back

No, you cannot add or subtract matrices of different dimensions. The matrices must have the same number of rows and columns.

Tags

CCSS.HSN.VM.C.8

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What is the associative property of matrix addition?

Back

The associative property of matrix addition states that for any matrices A, B, and C of the same dimensions, (A + B) + C = A + (B + C).