Question

Given matrices A, B, and C below (will attach image), perform the indicated operations if possible. If the operation is not possible, explain why.

A.) 2A+B
B.) 3B+C
C.) CA

I think for the first two yhu would multiply by the number given... But I'm not sure, and I don't know how I would multiply matrix C and A...

Answer 1

A.) scalar multiplication and then matrices addition
B.) same as above
C.) plain matrices multiplication

Answer 2

\(\large {
G
\begin{bmatrix}
a&b&c\\d&e&f
\end{bmatrix}\implies
\begin{bmatrix}
G\cdot a&G\cdot b&G\cdot c\\G\cdot d&G\cdot e&G\cdot f
\end{bmatrix}
\\ \quad \\
\begin{bmatrix}
a&b&c\\d&e&f
\end{bmatrix}+
\begin{bmatrix}
h&i&j\\k&l&m
\end{bmatrix}\implies
\begin{bmatrix}
a+h&b+i&c+j\\d+k&e+l&f+m
\end{bmatrix}
}\)

Answer 3

and for matrices multiplication
recall is row * column

Answer 4

Oh... And B... How would yhu do that?
Yhu would multiply all the terms by 3... but... Can yhu add B and C together?

Answer 5

a) is possible, since we can multiply 2A = by multiplying individual terms in the matrix A by 2. Meanwhile, 2A+B is alos possible, since we can add both results given that the order of 2A is same as thatof B. since order (row and columns of A) is 3x3 and that of B is also 3x3. I advise you to multiply every term in matrix A by 2 and add them termwise to the matrix B. That solves 2A+B!

Answer 6

b) is not possible, since §B will result in a 3x3 matrix, while C is a 1x3 matrix. U cannot add matrices with different number of rows or columns

Answer 7

For A, I got
2 4 3
7 1 9.6
2 22 8

Answer 8

CA is also possible, since C is of order 1x3, while A is of order 3x3. we can multiply matrices C whose columns is same as the rowns of A. i.e [1x3]x[3x3]

Answer 9

For C, would yhu multiply the first row... 3*0, 1*2, 5*-1
in that order all the way through?

Answer 10

I think so, u have to take each entry in C and multiply with corresponding row elements in A! then sum them up. your final answer should be a 1x3 matrix.

Answer 11

so it might be 3(2)+1(-3)+5(0) will be the element of the first row and first col. please check and do the rest.

Answer 12

Alright. Thank yhu again for the help! ^u^ I appreciate it. x3

Answer 13

If I give yhu a medal, can yhu do me a favor and give jdoe one? I can only give one medal, and they helped me too. ;o

Answer 14

sure thanks alot @Ria23

Answer 15

@Ria I cannot issue medals now may be later?

Answer 16

That's alright! That'll work ^.^ I just don't want jdoe's work and help to go unappreciated. Anytime would be fine. Thank yhu again for everything! n_n