Add & Subtract Matrices 1

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Precalculus

Matrices

Add & Subtract Matrices

Add & Subtract Matrices 1

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Question 1 of 4

1. Question
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$[[4],[-3],[5]]+[[2],[1],[0]]$
- 1. $[[6],[-2],[5]]$
- 2. $[[4],[-2],[7]]$
- 3. $[[2],[-4],[5]]$
- 4. $[[6],[2],[5]]$
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Two matrices can be added only if their dimensions ( $mtimesn$ ) are equal.

First, check the dimensions of each matrix

Matrix $1$ :

$[[4],[-3],[5]]$

rows $(m)=3$

columns $(n)=1$

Dimension $(mtimesn)=$ $3xx1$

Matrix $2$ :

$[[2],[1],[0]]$

rows $(m)=3$

columns $(n)=1$

Dimension $(mtimesn)=$ $3xx1$

Since their dimensions are equal, these two matrices can be added

Next, add the matrices by simply adding each matching elements

$[[4],[-3],[5]]+[[2],[1],[0]]$

$=$ $[[ 4+2],[-3+1],[ 5+0]]$

$=$ $[[6],[-2],[5]]$

$[[6],[-2],[5]]$
Question 2 of 4

2. Question
Solve for $x+y$ given that:

$x=[[4,2],[3,5]]$ $y=[[4,-2],[-2,1]]$ $z=[[-5,6],[-1,-2]]$
- 1. $[[0,2],[1,5]]$
- 2. $[[8,0],[1,6]]$
- 3. $[[8,6]]$
- 4. $[[-8,0],[1,-6]]$
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Two matrices can be added only if their dimensions ( $mtimesn$ ) are equal.

First, check the dimensions of each matrix

Matrix $x$ :

$x=[[4,2],[3,5]]$

rows $(m)=2$

columns $(n)=2$

Dimension $(mtimesn)=$ $2xx2$

Matrix $y$ :

$y=[[4,-2],[-2,1]]$

rows $(m)=2$

columns $(n)=2$

Dimension $(mtimesn)=$ $2xx2$

Since their dimensions are equal, these two matrices can be added

Next, add the matrices by simply adding each matching elements

$x+y$ $=$ $[[4,2],[3,5]]+[[4,-2],[-2,1]]$

$=$ $[[4+4,2+(-2)],[3+(-2),5+1]]$

$=$ $[[8,0],[1,6]]$

$[[8,0],[1,6]]$

Question 3 of 4

Solve for

$x+y+z$ given that:

$x=[[4,2],[3,5]]$

$y=[[4,-2],[-2,1]]$

$z=[[-5,6],[-1,-2]]$

1. $[[3,8],[0,1]]$
2. $[[6,2],[0,5]]$
3. $[[3],[0]]$
4. $[[3,6],[0,4]]$

Question 4 of 4

4. Question
Solve for $x+y$ given that:

$x=[[2,3,4],[4,5,1]]$ $y=[[3,2,4],[0,4,6]]$ $z=[[4,2],[5,9]]$
- 1. $[[5,5,8],[4,9,7]]$
- 2. $[[4,5],[9,7]]$
- 3. $[[2,5,4],[3,9,0]]$
- 4. $[[5,2,8]]$
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Two matrices can be added only if their dimensions ( $mtimesn$ ) are equal.

First, check the dimensions of each matrix

Matrix $x$ :

$x=[[2,3,4],[4,5,1]]$

rows $(m)=2$

columns $(n)=3$

Dimension $(mtimesn)=$ $2xx3$

Matrix $y$ :

$y=[[3,2,4],[0,4,6]]$

rows $(m)=2$

columns $(n)=3$

Dimension $(mtimesn)=$ $2xx3$

Since their dimensions are equal, these two matrices can be added

Next, add the matrices by simply adding each matching elements

$x+y$ $=$ $[[2,3,4],[4,5,1]]+[[3,2,4],[0,4,6]]$

$=$ $[[2+3,3+2,4+4],[4+0,5+4,1+6]]$

$=$ $[[5,5,8],[4,9,7]]$

$[[5,5,8],[4,9,7]]$

Add & Subtract Matrices 1

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Quiz summary

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1. Question

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2. Question

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3. Question

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4. Question

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Quizzes

	$[[4],[-3],[5]]+[[2],[1],[0]]$

$=$	$[[ 4+2],[-3+1],[ 5+0]]$

$=$	$[[6],[-2],[5]]$

$x+y$	$=$	$[[4,2],[3,5]]+[[4,-2],[-2,1]]$

	$=$	$[[4+4,2+(-2)],[3+(-2),5+1]]$

	$=$	$[[8,0],[1,6]]$

$x+y+z$	$=$	$[[4,2],[3,5]]+[[4,-2],[-2,1]]+[[-5,6],[-1,-2]]$

	$=$	$[[4+4+(-5),2+(-2)+6],[3+(-2)+(-1),5+1+(-2)]]$

	$=$	$[[3,6],[0,4]]$

$x+y$	$=$	$[[2,3,4],[4,5,1]]+[[3,2,4],[0,4,6]]$

	$=$	$[[2+3,3+2,4+4],[4+0,5+4,1+6]]$

	$=$	$[[5,5,8],[4,9,7]]$