- #1

flash

- 68

- 0

I'm not quite sure what the question is asking. I think I just need someone to point me in the right direction.

Thanks

You are using an out of date browser. It may not display this or other websites correctly.

You should upgrade or use an alternative browser.

You should upgrade or use an alternative browser.

- Thread starter flash
- Start date

- #1

flash

- 68

- 0

I'm not quite sure what the question is asking. I think I just need someone to point me in the right direction.

Thanks

- #2

tiny-tim

Science Advisor

Homework Helper

- 25,838

- 256

Hi flash!

Hint: AC = I … so multiply something by I !

Hint: AC = I … so multiply something by I !

- #3

Defennder

Homework Helper

- 2,592

- 5

Further hint if the one given above is too vague: Multiply it on the right side of I.

- #4

HallsofIvy

Science Advisor

Homework Helper

- 43,021

- 971

If AC= I then CA= I.

How would you solve Ax= b if A, x, and b were NUMBERS?

How would you solve Ax= b if A, x, and b were NUMBERS?

- #5

flash

- 68

- 0

Ax = b

CAx = Cb

Ix = Cb

x = Cb

Am I on the right track?

CAx = Cb

Ix = Cb

x = Cb

Am I on the right track?

- #6

tiny-tim

Science Advisor

Homework Helper

- 25,838

- 256

Am I on the right track?

Not only on the right track … you've arrived at Grand Central!

You have proved that A sends Cb to ACb = Ib = b.

So A(Cb) = b.

In other words, x = Cb is a solution to Ax = b.

- #7

flash

- 68

- 0

A is a 4x3 matrix

C is a 3x4 matrix such that CA = I

Suppose, for some given b in R4 that Ax=b has at least one solution. Show that this solution is unique.

Can I just say x = Cb which implies that there is only one solution for x? I'm thinking that I should say something along the lines of: if there exists a C such that CA = I then A must have no free variables.

- #8

BryanP

- 195

- 0

- #9

HallsofIvy

Science Advisor

Homework Helper

- 43,021

- 971

A is a 4x3 matrix

C is a 3x4 matrix such that CA = I

Suppose, for some given b in R4 that Ax=b has at least one solution. Show that this solution is unique.

Can I just say x = Cb which implies that there is only one solution for x? I'm thinking that I should say something along the lines of: if there exists a C such that CA = I then A must have no free variables.

Yes, that's all you need to do. C is a given matrix , b is a given vector: since multiplication of a 3x4 matrix with a 4 dimensional vector (a 4x1 matrix) is "well defined", x= Cb must be a specific, unique vector.

(I

Last edited by a moderator:

- #10

BryanP

- 195

- 0

(IthinkBryanP's response is to your previous question- though then I don't know why he refers to " the number of solutions for every b in Ax = b". Here, A isnotinvertible. Only square matrices are invertible.)

I apologize for that. I didn't notice my error about the invertibility.

Share:

- Replies
- 9

- Views
- 326

- Last Post

- Replies
- 7

- Views
- 403

- Replies
- 57

- Views
- 965

- Last Post

- Replies
- 10

- Views
- 1K

- Last Post

- Replies
- 31

- Views
- 997

- Replies
- 24

- Views
- 566

- Last Post

- Replies
- 16

- Views
- 774

- Last Post

- Replies
- 6

- Views
- 902

- Replies
- 4

- Views
- 637

- Last Post

- Replies
- 15

- Views
- 447