Question

find the matrix A if :

2A - [1 0 -2]T = [2 0
[ 4 7 3 ] -3 4
0 8]

anyone?

Answer 1

First do the \(T\) operation.

Answer 2

you mean transform the T?

Answer 3

@wio

Answer 4

It is transpose operation.

Answer 5

do you know how to transpose a matrix?

Answer 6

opss sorry typo . it would be like this? [ 4 1
7 0
3 -2 ]

@wio

Answer 7

yes

Answer 8

now add it to both sides.

Answer 9

then?

Answer 10

then multiply both sides by \(1/2\)

Answer 11

can you give me example? @wio

Answer 12

You don't know how to add matrices?

Answer 13

This is no different than algebra. You're just using matrix operations instead.

Answer 14

after i get like this [ 4 1 now i need to multiply to this matrix [2 0
7 0 -3 4
3 -2 ] 0 8]

Answer 15

@wio

Answer 16

No, you add it to both sides.

Answer 17

okay so it would be like this right? [6 1
4 4
3 6]
so the next step ? @wio

Answer 18

Yes, so you have \[
2A = \begin{bmatrix}6&1\\4&4\\3&6\end{bmatrix}
\]

Answer 19

Now you solve for \(A\) using scalar multiplication.

Answer 20

okay,you mean like this : 2A = 2 . [ 6 1 [ 12 2
4 4 = 8 8
3 6 ] 6 12]

like this ? @wio

Answer 21

If you multiply both sides by \(2\), then \(2\times 2A = 4A\) and you still haven't isolated \(A\).

Answer 22

so how to solve A using scalar multiplication?

@wio

Answer 23

Okay, we want \(c\) where \(c\times 2 = 1\). So what is \(c\)?

Answer 24

1/2 @wio

Answer 25

so now how to solve A? @wio

Answer 26

Multiply both sides by \(1/2\).

Answer 27

i get this = [ 3 1/2
2 2
3/2 3]

is it true? @wio

Answer 28

Yes

Answer 29

then,next step? @wio

Answer 30

You have found \(A\). What more do you want?

Answer 31

so that's all? @wio

Answer 32

thank you for helping @wio