How do I solve for column vector from a matrix

Hello,

I want to find column matrix [a1 a2]'

[a1 a2]'*[a1 a2] = [1 0; 1 0];

how do I do that?

thanks

[Matt J]

There is no solution to the equation you've shown. The left hand side is a symmetric matrix. The right hand side is not.

[Suma]

for example, take a1=1, a2=0

[1 0]'*[1 0] = [1 0; 0 0]

But the matrix(RHS) could be anything, isn't it possible to solve this?

[Matt J]

But the matrix(RHS) could be anything, isn't it possible to solve this?

Nope.

[Suma]

notice that [a1 a2]' is a column vector and [a1 a2] a row vector which are being multiplied

[Matt J]

Yep. In addition to being symmetric, the left hand side expression is also rank 1. That means the right hand side would at least have to have those same properties.

Answer 1

[Jos (10584)]

(1) [a ; b] * [a b] = [a*a a*b ; b*a b*b] % by definition

(2) [a ; b] * [a b] = [1 0 ; 1 0]  % by request

=> b*b = 0 => b is 0    
   b*a = 1 => b is not 0

Impossible!