For the given matrices A and B find each of the following. (a) A+B (b) B+A (c) A-B A=[ 2

For the given matrices A and B find each of the following....

For the given matrices $A$ and $B$ find each of the following. (a) $\boldsymbol{A}+\boldsymbol{B} \quad$ (b) $\boldsymbol{B}+\boldsymbol{A} \quad(\boldsymbol{c}) \boldsymbol{A}-\boldsymbol{B}$ $$A=\left[\begin{array}{rr}2 & -4 \\-1 & \frac{1}{2} \\3 & -2\end{array}\right]$$ $$B=\left[\begin{array}{rr}5 & 0 \\3 & \frac{1}{2} \\-1 & 1\end{array}\right]$$

For the given matrices $A$ and $B$ find each of the following.
(a) $\boldsymbol{A}+\boldsymbol{B} \quad$ (b) $\boldsymbol{B}+\boldsymbol{A} \quad(\boldsymbol{c}) \boldsymbol{A}-\boldsymbol{B}$
$$A=\left[\begin{array}{rr}2 & -4 \\-1 & \frac{1}{2} \\3 & -2\end{array}\right]$$
$$B=\left[\begin{array}{rr}5 & 0 \\3 & \frac{1}{2} \\-1 & 1\end{array}\right]$$

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Matrix Subtraction

Matrix subtraction is performed by subtracting corresponding elements of two matrices of the same size. Unlike addition, subtraction is not commutative, meaning A - B generally does not equal B - A. The operation requires the matrices to have the same dimensions for it to be valid.

Dimension Compatibility

For both matrix addition and subtraction, it is essential that the matrices involved have the same number of rows and columns. This compatibility ensures that each element in one matrix has a corresponding element in the other matrix to be added or subtracted.

Matrix Addition

Matrix addition is an operation where two matrices of the same dimension are added element-wise. Each element in the resulting matrix is the sum of the corresponding elements from the original matrices, and the operation's validity depends on both matrices having identical dimensions.

Commutative Property of Addition

The commutative property in the context of matrix addition states that the order in which matrices are added does not affect the result. That is, A + B is equal to B + A, provided that both matrices have the same dimensions.

Transcript

00:01 Okay, let's say that you're given the matrix a, which is a three row by two column matrix, and matrix b, which is also a three row by two column matrix.

00:14 Okay, and let's say that you're asked to add a plus b.

00:18 Hey, the first thing you need to do before you can add matrices is to make sure that the matrix are the same dimension.

00:25 And in this case, they both are.

00:28 Okay, and then when you go to add, what you have to do, is just make sure you keep everything in its current position.

00:37 Okay, so we're going to first start with a, because that's what they start with.

00:40 So we're going to just rewrite this matrix.

00:45 Again, keeping everything in the correct row and column.

00:49 Now let's look at the b.

00:51 Okay, so again, i'm going to look at the first column first, and i'm just going to add on row one, add row two, add row three.

01:00 Okay, now let's look at the second column.

01:02 We're going to add that on, so i'm going to add row one, row two, row three.

01:11 Okay, and so when we add these together, we find our solution is 7, 2, 2, and then negative 4, 1, negative 1.

01:27 And what you're going to notice is your solution is also a 3 by 2, and that should stay the same.

01:35 Okay, so now let's try b plus a.

01:42 How we go about adding it is the same process...

Please give Ace some feedback