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Matrix Operations Calculator

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Example
Created on 2024-06-20Asked by Harper Robinson (Solvelet student)
Perform the matrix operations for A=(1234)andB=(5678). A = \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix} \quad \text{and} \quad B = \begin{pmatrix} 5 & 6 \\ 7 & 8 \end{pmatrix}. Calculate A+B A + B and AB AB .

Solution

Given the matrices A=(1234)andB=(5678), A = \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix} \quad \text{and} \quad B = \begin{pmatrix} 5 & 6 \\ 7 & 8 \end{pmatrix}, we will calculate A+B A + B and AB AB . 1. Calculate A+B A + B : A+B=(1234)+(5678)=(1+52+63+74+8)=(681012) A + B = \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix} + \begin{pmatrix} 5 & 6 \\ 7 & 8 \end{pmatrix} = \begin{pmatrix} 1+5 & 2+6 \\ 3+7 & 4+8 \end{pmatrix} = \begin{pmatrix} 6 & 8 \\ 10 & 12 \end{pmatrix} 2. Calculate AB AB : AB=(1234)(5678)=(1⋅5+2⋅71⋅6+2⋅83⋅5+4⋅73⋅6+4⋅8)=(5+146+1615+2818+32)=(19224350) AB = \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix} \begin{pmatrix} 5 & 6 \\ 7 & 8 \end{pmatrix} = \begin{pmatrix} 1 \cdot 5 + 2 \cdot 7 & 1 \cdot 6 + 2 \cdot 8 \\ 3 \cdot 5 + 4 \cdot 7 & 3 \cdot 6 + 4 \cdot 8 \end{pmatrix} = \begin{pmatrix} 5 + 14 & 6 + 16 \\ 15 + 28 & 18 + 32 \end{pmatrix} = \begin{pmatrix} 19 & 22 \\ 43 & 50 \end{pmatrix} Therefore, the results of the matrix operations are: A+B=(681012)andAB=(19224350) A + B = \begin{pmatrix} 6 & 8 \\ 10 & 12 \end{pmatrix} \quad \text{and} \quad AB = \begin{pmatrix} 19 & 22 \\ 43 & 50 \end{pmatrix} Solved on Solvelet with Basic AI Model
Some of the related questions asked by Theodore Thompson on Solvelet
1. Multiply the matrices A=[1234] A = \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix} and B=[−102−3] B = \begin{bmatrix} -1 & 0 \\ 2 & -3 \end{bmatrix} .2. Calculate the determinant of the product of matrices C=ABC = AB, where A=[123456]A = \begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \end{bmatrix} and B=[−102−312]B = \begin{bmatrix} -1 & 0 \\ 2 & -3 \\ 1 & 2 \end{bmatrix}.
DefinitionThe matrix operations include its addition,subtraction, scalar multiplication and matrix multiplication and so on. Many of these operations have properties, or rules of operation. Case in point: the sum of the matrices A=(13​24​) and B=(57​68​) is A+B=(610​812​)
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