Adding & Subtracting Matrices 2
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Question 1 of 4
1. Question
Solve for `x+z` given that:`x=[[2,3,4],[4,5,1]]` `y=[[3,2,4],[0,4,6]]` `z=[[4,2],[5,9]]`Hint
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Two matrices can be added only if their dimensions (`mtimesn`) are equal.First, check the dimensions of each matrixMatrix `x`:`x=[[2,3,4],[4,5,1]]`rows`(m)=2`columns`(n)=3`Dimension`(mtimesn)=``2xx3`Matrix `y`:`z=[[4,2],[5,9]]`rows`(m)=2`columns`(n)=2`Dimension`(mtimesn)=``2xx2`Since their dimensions are not equal, these two matrices cannot be addedno solution -
Question 2 of 4
2. Question
Solve`[[-5,-3,6],[-1,0,-2]]+[[-1,-2,8],[7,10,-5]]`Hint
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Two matrices can be added only if their dimensions (`mtimesn`) are equal.First, check the dimensions of each matrixMatrix `1`:`[[-5,-3,6],[-1,0,-2]]`rows`(m)=2`columns`(n)=3`Dimension`(mtimesn)=``2xx3`Matrix `2`:`[[-1,-2,8],[7,10,-5]]`rows`(m)=2`columns`(n)=3`Dimension`(mtimesn)=``2xx3`Since their dimensions are equal, these two matrices can be addedNext, add the matrices by simply adding each matching elements`[[-5,-3,6],[-1,0,-2]]+[[-1,-2,8],[7,10,-5]]` `=` `[[-5+(-1),-3+(-2),6+8],[-1+7,0+10,-2+(-5)]]` `=` `[[-6,-5,14],[6,10,-7]]` `[[-6,-5,14],[6,10,-7]]` -
Question 3 of 4
3. Question
Solve`[[7,5],[3,0]]-[[3,-6],[4,-1]]`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`:`[[7,5],[3,0]]`rows`(m)=2`columns`(n)=2`Dimension`(mtimesn)=``2xx2`Matrix `2`:`[[3,-6],[4,-1]]`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`[[7,5],[3,0]]-[[3,-6],[4,-1]]` `=` `[[7-3,5-(-6)],[3-4,0-(-1)]]` `=` `[[4,11],[-1,1]]` `[[4,11],[-1,1]]` -
Question 4 of 4
4. Question
Solve`[[14,-3,2],[-1,9,-7],[5,-1,8]]-[[4,6,-10],[9,1,7],[-2,-3,9]]`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`:`[[14,-3,2],[-1,9,-7],[5,-1,8]]`rows`(m)=3`columns`(n)=3`Dimension`(mtimesn)=``3xx3`Matrix `2`:`[[4,6,-10],[9,1,7],[-2,-3,9]]`rows`(m)=3`columns`(n)=3`Dimension`(mtimesn)=``3xx3`Since their dimensions are equal, these two matrices can be subtractedNext, subtract the matrices by simply subtracting each matching elements`[[14,-3,2],[-1,9,-7],[5,-1,8]]-[[4,6,-10],[9,1,7],[-2,-3,9]]` `=` `[[14-4,-3-6,2-(-10)],[-1-9,9-1,-7-7],[5-(-2),-1-(-3),8-9]]` `=` `[[10,-9,12],[-10,8,-14],[7,2,-1]]` `[[10,-9,12],[-10,8,-14],[7,2,-1]]`
Quizzes
- Adding & Subtracting Matrices 1
- Adding & Subtracting Matrices 2
- Adding & Subtracting Matrices 3
- Multiplying Matrices 1
- Multiplying Matrices 2
- Multiplication Word Problems
- Determinant of a Matrix
- Inverse of a Matrix
- Solving Systems of Equations 1
- Solving Systems of Equations 2
- Gauss Jordan Elimination
- Cramer’s Rule