Multiply Matrices 1
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Question 1 of 4
1. Question
Solve for `2A` given that:`A=[[6,-14],[18,10]]`Hint
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A constant multiplied to a matrix is simply distributed to each of the elements.Substitute matrix `A` to `2A` and solve.`A=[[6,-14],[18,10]]``2A` `=` `2[[6,-14],[18,10]]` Substitute `A` `=` `[[2xx6,2xx-14],[2xx18,2xx10]]` Distribute `2` `=` `[[12,-28],[36,20]]` `[[12,-28],[36,20]]` -
Question 2 of 4
2. Question
Solve for `-1/2A` given that:`A=[[6,-14],[18,10]]`Hint
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A constant multiplied to a matrix is simply distributed to each of the elements.Substitute matrix `A` to `-1/2A` and solve.`A=[[6,-14],[18,10]]``-1/2A` `=` `-1/2[[6,-14],[18,10]]` Substitute `A` `=` \begin{bmatrix}
-\frac{1}{2}\times6 & -\frac{1}{2}\times-14 \\[0.3em]
-\frac{1}{2}\times18 & -\frac{1}{2}\times10 \\
\end{bmatrix}Distribute `-1/2` `=` `[[-3,7],[-9,-5]]` `[[-3,7],[-9,-5]]` -
Question 3 of 4
3. Question
Solve`[[1,3,2]]times[[6,1,0],[0,3,1],[1,2,2]]`Hint
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Multiplying Two Matrices
`[[a,b,c]]xx[[p],[q],[r]]=ap+bq+cr`Two matrices can be multiplied only if the number of columns (`n`) in the first matrix is equal to the number of rows
(`m`) in the second matrix.First, check the dimensions of each matrixMatrix `1`:`[[1,3,2]]`rows(`m`)`=1`columns(`n`)`=3`Dimension`(mtimesn)=1xx``3`Matrix `2`:`[[6,1,0],[0,3,1],[1,2,2]]`rows(`m`)`=3`columns(`n`)`=3`Dimension`(mtimesn)=``3``xx3`Since the number of columns in the first matrix (`3`) and the number of rows in the second matrix
(`3`) are equal, these two matrices can be multipliedNext, proceed with multiplying the two matrices`[[1,3,2]]times``[[6,1,0],[0,3,1],[1,2,2]]` `=` \begin{bmatrix}
((1\cdot\color{#9a00c7}{6})+(3\cdot\color{#9a00c7}{0})+(2\cdot\color{#9a00c7}{1})) & ((1\cdot\color{#9a00c7}{1})+(3\cdot\color{#9a00c7}{3})+(2\cdot\color{#9a00c7}{2})) & ((1\cdot\color{#9a00c7}{0})+(3\cdot\color{#9a00c7}{1})+(2\cdot\color{#9a00c7}{2})) \\
\end{bmatrix}`=` `[[6+0+2,1+9+4,0+3+4]]` `=` `[[8,14,7]]` `[[8,14,7]]` -
Question 4 of 4
4. Question
Solve`[[2,6,-2,7],[1,0,3,1]]times[[3],[-1],[4],[6]]`Hint
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Fantastic!
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Multiplying Two Matrices
`[[a,b,c]]xx[[p],[q],[r]]=ap+bq+cr`Two matrices can be multiplied only if the number of columns (`n`) in the first matrix is equal to the number of rows
(`m`) in the second matrix.First, check the dimensions of each matrixMatrix `1`:`[[2,6,-2,7],[1,0,3,1]]`rows(`m`)`=2`columns(`n`)`=4`Dimension`(mtimesn)=2xx``4`Matrix `2`:`[[3],[-1],[4],[6]]`rows(`m`)`=4`columns(`n`)`=1`Dimension`(mtimesn)=``4``xx1`Since the number of columns in the first matrix (`4`) and the number of rows in the second matrix
(`4`) are equal, these two matrices can be multipliedNext, proceed with multiplying the two matrices`[[2,6,-2,7],[1,0,3,1]]times``[[3],[-1],[4],[6]]` `=` \begin{bmatrix}
(2\cdot\color{#9a00c7}{3})+(6\cdot\color{#9a00c7}{-1})+(-2\cdot\color{#9a00c7}{4})+(7\cdot\color{#9a00c7}{6}) \\[0.3em]
(1\cdot\color{#9a00c7}{3})+(0\cdot\color{#9a00c7}{-1})+(3\cdot\color{#9a00c7}{4})+(1\cdot\color{#9a00c7}{6})
\end{bmatrix}`=` `[[6+(-6)+(-8)+42],[3+0+12+6]]` `=` `[[34],[21]]` `[[34],[21]]`
Quizzes
- Add & Subtract Matrices 1
- Add & Subtract Matrices 2
- Add & Subtract Matrices 3
- Multiply Matrices 1
- Multiply Matrices 2
- Matrices: Multiplication Word Problems
- Determinant of a Matrix
- Inverse of a Matrix
- Matrices: Systems of Equations 1
- Matrices: Systems of Equations 2
- Gauss Jordan Elimination
- Cramer’s Rule