How Can Any Scalar Lambda Solve B*(x + Lambda*v) = b in Matlab?

[playboy]

Homework Statement

In Matlab,

Find the scalar (lamda) for which x+(lamda)v equals the solution obtained with the backslash operator \. Hence, x=B\b in matlab

(This is another way of finding the inverse inv(B)... we could also use x=B\b)

Homework Equations

We have Bx = b

B =
[-1 2 -3
0 4 1
3 -6 9]

b = [-12 -1 36]

Null space v=[-14 -1 4]

x = [-12.0000, -0.2143, -0.1429] <--- from B\b in matlab

The Attempt at a Solution

B*(x + (lamda)v) = b
Bx + (lamda)Bv = b

since v is the null space (lamda)Bv=0

therefore, (lamda) could be anything?

Is that correct?

 

[mighty2000]

Thank you for your question. Yes, your reasoning is correct. Since v is in the null space of B, any scalar multiple of v will also be in the null space. Therefore, (lamda) can be any value and still satisfy the equation Bx + (lamda)Bv = b. This means that there is no unique scalar that will result in the same solution as using the backslash operator. However, if you want to use the inverse method, you can still use x = B\b to obtain the same solution. I hope this helps clarify your understanding. Good luck with your studies!