Add & Subtract Matrices 3
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Question 1 of 4
1. Question
Solve`[[1/2,1/3],[3,7]]-[[4,-2/3],[1/2,2]]`Hint
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Two matrices can be subtracted only if their dimensions (`mtimesn`) are equal.First, check the dimensions of each matrixMatrix `1`:\begin{bmatrix}
\frac{1}{2} & \frac{1}{3} \\[0.3em]
3 & 7
\end{bmatrix}rows`(m)=2`columns`(n)=2`Dimension`(mtimesn)=``2xx2`Matrix `2`:\begin{bmatrix}
4 & -\frac{2}{3} \\[0.3em]
\frac{1}{2} & 2
\end{bmatrix}rows`(m)=2`columns`(n)=2`Dimension`(mtimesn)=``2xx2`Since their dimensions are equal, these two matrices can be subtractedNext, subtract the matrices by simply subtracting each matching elements\begin{bmatrix}
\frac{1}{2} & \frac{1}{3} \\
3 & 7
\end{bmatrix}$$-$$\begin{bmatrix}
4 & -\frac{2}{3} \\
\frac{1}{2} & 2
\end{bmatrix}`=` \begin{bmatrix}
\frac{1}{2}-4 & \frac{1}{3}-(-\frac{2}{3}) \\[0.3em]
3-\frac{1}{2} & 7-2
\end{bmatrix}`=` \begin{bmatrix}
-\frac{7}{2} & 1 \\[0.3em]
\frac{5}{2} & 5
\end{bmatrix}\begin{bmatrix}
-\frac{7}{2} & 1 \\[0.3em]
\frac{5}{2} & 5
\end{bmatrix} -
Question 2 of 4
2. Question
Solve`[[0.4,0.9],[1.5,-3.2]]-[[0.6,-0.8],[-1,1.7]]`Hint
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Keep Going!
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Two matrices can be subtracted only if their dimensions (`mtimesn`) are equal.First, check the dimensions of each matrixMatrix `1`:`[[0.4,0.9],[1.5,-3.2]]`rows`(m)=2`columns`(n)=2`Dimension`(mtimesn)=``2xx2`Matrix `2`:`[[0.6,-0.8],[-1,1.7]]`rows`(m)=2`columns`(n)=2`Dimension`(mtimesn)=``2xx2`Since their dimensions are equal, these two matrices can be subtractedNext, subtract the matrices by simply subtracting each matching elements`[[0.4,0.9],[1.5,-3.2]]-[[0.6,-0.8],[-1,1.7]]` `=` `[[0.4-0.6,0.9-(-0.8)],[1.5-(-1),-3.2-1.7]]` `=` `[[-0.2,1.7],[2.5,-4.9]]` `[[-0.2,1.7],[2.5,-4.9]]` -
Question 3 of 4
3. Question
Solve`[[2,5,-7],[3,6,-1]]-[[-1,-3,9],[2,4,-5]]`Hint
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Great Work!
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Two matrices can be subtracted only if their dimensions (`mtimesn`) are equal.First, check the dimensions of each matrixMatrix `1`:`[[2,5,-7],[3,6,-1]]`rows`(m)=2`columns`(n)=3`Dimension`(mtimesn)=``2xx3`Matrix `2`:`[[-1,-3,9],[2,4,-5]]`rows`(m)=2`columns`(n)=3`Dimension`(mtimesn)=``2xx3`Since their dimensions are equal, these two matrices can be subtractedNext, subtract the matrices by simply subtracting each matching elements`[[2,5,-7],[3,6,-1]]-[[-1,-3,9],[2,4,-5]]` `=` `[[2-(-1),5-(-3),-7-9],[3-2,6-4,-1-(-5)]]` `=` `[[3,8,-16],[1,2,4]]` `[[3,8,-16],[1,2,4]]` -
Question 4 of 4
4. Question
Solve for `z+y-x` given that:`x=[[4,2],[3,5]]` `y=[[4,-2],[-2,1]]` `z=[[-5,6],[-1,-2]]`Hint
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Exceptional!
Incorrect
Matrices can be added or subtracted only if their dimensions (`mtimesn`) are equal.First, check the dimensions of each matrixMatrix `x`:`x=[[4,2],[3,5]]`rows`(m)=2`columns`(n)=2`Dimension`(mtimesn)=``2xx2`Matrix `y`:`y=[[4,-2],[-2,1]]`rows`(m)=2`columns`(n)=2`Dimension`(mtimesn)=``2xx2`Matrix `z`:`z=[[-5,6],[-1,-2]]`rows`(m)=2`columns`(n)=2`Dimension`(mtimesn)=``2xx2`Since their dimensions are equal, these two matrices can be added and subtractedNext, add the matrices by simply adding and then subtracting each matching elements`z+y-x` `=` `[[-5,6],[-1,-2]]+[[4,-2],[-2,1]]-[[4,2],[3,5]]` `=` `[[-5+4-4,6+(-2)-2],[-1+(-2)-3,-2+1-5]]` `=` `[[-5,2],[-6,-6]]` `[[-5,2],[-6,-6]]`
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