Question

A and X is 4x4 matrix. AX=E-2X. Find X.

Answer 1

Add 2X both the sides first...

Answer 2

\[AX + 2X = E - 2X + 2X\]
\[AX + 2X = E\]

Answer 3

Can you tell me what is E here??

A matrix or something else..??

Answer 4

When you will take common X from AX + 2X then you will be using Identity matrix that is I:

\[X(A + 2I) = E\]

Answer 5

im not sure
the answer is X=(A+2E)inverse(-1)

Answer 6

want to know why A+2E

Answer 7

And now to find X, you will take inverse of \((A + 2I)\)

So, you will get :

\[X = (A+2I)^{-1} \cdot E\]

Answer 8

Do you know we can add two matrices having same rows and columns ??

Answer 9

Suppose you have A and B matrices of 3x3 dimension:

You can add, subtract these matrices..

Right ???

Answer 10

yes

Answer 11

Remember one thing : You can add or subtract two matrices if they have same dimensions..

But you cannot add a matrix with a number like 2 ;

I show you :

A + 2 = ???

Answer 12

Here, you can't add a matrix with a number:

However, you can add two matrices..

Answer 13

To make 2 as matrix, we multiply it with identity matrix (E or I) having same dimension of the matrix we are adding it to...

Answer 14

Getting ??

Answer 15

so is E the identity matrix?

Answer 16

@hartnn will help you here...

Electricity has gone here... Ha ha ha...

Here, In India, Identity matrix is shown by I...

Answer 17

i study in China. Math here is wierd and hard

Answer 18

i kind of get what you said

Answer 19

AX=E-2X
to get matrix 2 that makes (A+2E)X=E then
X=(A+2E)inverse

Answer 20

u got that correct @mxgforce