Matrices Calculator

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Example

Created on 2024-06-20Asked by Mateo Johnson (Solvelet student)

Given the matrices

A = \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix} \quad \text{and} \quad B = \begin{pmatrix} 2 & 0 \\ 1 & 3 \end{pmatrix},

calculate the product

AB

Solution

To calculate the product

AB

of the matrices

A = \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix} \quad \text{and} \quad B = \begin{pmatrix} 2 & 0 \\ 1 & 3 \end{pmatrix},

we use matrix multiplication: 1. Multiply the rows of

A

by the columns of

B

AB = \begin{pmatrix} 1 \cdot 2 + 2 \cdot 1 & 1 \cdot 0 + 2 \cdot 3 \\ 3 \cdot 2 + 4 \cdot 1 & 3 \cdot 0 + 4 \cdot 3 \end{pmatrix}

2. Perform the calculations:

AB = \begin{pmatrix} 2 + 2 & 0 + 6 \\ 6 + 4 & 0 + 12 \end{pmatrix}

AB = \begin{pmatrix} 4 & 6 \\ 10 & 12 \end{pmatrix}

Therefore, the product

AB

is:

AB = \begin{pmatrix} 4 & 6 \\ 10 & 12 \end{pmatrix}

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Some of the related questions asked by Avery Green on Solvelet

1. Add the matrices

A = \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}

and

B = \begin{bmatrix} -1 & 0 \\ 2 & -3 \end{bmatrix}

.2. Find the determinant of the matrix

C = \begin{bmatrix} 2 & 1 & -3 \\ 0 & -2 & 1 \\ 1 & 2 & 0 \end{bmatrix}

DefinitionA matrix is a rectangular table of numbers, symbols, or expressions displayed in rows and columns. They represent transformations, solve systems of equations, and do many other things in algebra. Examples of matrices include matrix addition and subtraction and matrix multiplication, matrix determinants and matrix inverses.

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