Question

question will be attached

Given the matrices A and B below, find A + B and 3A

Answer 1

We add matrices by adding the corresponding elements. We multiply by a scalar by multiplying every element with the scalar.

Answer 2

so i just add them like the #s in the same rows and what do i do about the 3A? @beginnersmind

Answer 3

And just to clarify if you don't know what "corresponding elements" are, it means the (i,j) spot of both matrices A and B, where i is the row and j is the column. So you would take row i and column j of A and add it with row i and column j of B. For example, row 1 and column 1 (i=1, j=1) of your A matrix is 2 and row 1 column 1 of your B matrix is 1, so you would add 2+1=3 so 3 would be the value you would put in the spot of row 1, column 1 of your solution matrix. Then on to the next spot, row 1 and column 2 of A is -3 and row 1 and column 2 of B is 0, so adding them is 1+0=1 so 1 would be the value you would put in the spot of row 1, column 2 of your solution matrix. And so on.

Answer 4

So here is a slightly different version of your problem just to show the method:\[\left[\begin{matrix}2 & -3 \\ 0 & 5\end{matrix}\right] + \left[\begin{matrix}1 & 0 \\ 10 & -1/2\end{matrix}\right] = \left[\begin{matrix}2+1 & -3+0 \\ 0+10 & 5-1/2\end{matrix}\right] = \left[\begin{matrix}3 & -3 \\ 10 & 9/2\end{matrix}\right]\]

Answer 5

oh i see but what does the 3A part mean

Answer 6

For the 3A, beginnersmind told you how to do it: just multiply the scalar, 3, by every element in A. An "element" is just one spot. For example in my above problem I have four spots, or four "elements" by which to multiply the 3. So:\[3\left[\begin{matrix}2 & -3 \\ 0 & 5\end{matrix}\right]=\left[\begin{matrix}2*3 & -3*3 \\ 0*3 & 5*3\end{matrix}\right] = \left[\begin{matrix}6 & -9 \\ 0 & 15\end{matrix}\right]\]

Answer 7

oh ok so I only do that to the matrix A

Answer 8

If it says to find 3A, then yes just do 3 multiplied by the matrix A, B has nothing to do with it.

Answer 9

for A+B [10 1] for the last part

[21 -6] for 3A

Answer 10

[10 -1] actually, because you are adding -2+1, which is -1.
And yes, [21 -6] for the last part of 3A, you got it.

Answer 11

oh yeahh sorry

thank you!! :)