Question

Linear Algebra,

Determine a constant 'k' such that

(kA)^T * (kA) = 1

A = -2
1
-1


Are there more than one such constants ?

Answer 1

[-2k k -k] [-2k ]
[ k ] = 4k^2 +k^2 +k^2 = 1
[ -k ]

got that?

Answer 2

yes @hartnn

Answer 3

so you'll get 2 values of k from there ..

Answer 4

@hartnn is it true that if a homogeneous system has at least one more solution than the trivial one, then it has infinitely many solutions ?

Answer 5

a homogeneous system,
either has no solution
or only trivial solution
or infinitely many solutions

Answer 6

could be non square and stil hve the same properties, right ?

Answer 7

yes

Answer 8

Do you still need help on this problem?

Answer 9

^^

Answer 10

I suggest not distributing k to the elements of the vector,

\[(kA)^\top kA = 1\]
\[k^2 A^\top A = 1\]
\[k^2 = \frac{1}{A^\top A}\]
\[k = \frac{\pm 1}{\sqrt{A^\top A}}\]

Don't let the matrix notation confuse you, \(A^\top A \) is just the dot product of the vector A with itself, and the dot product is a scalar.

Answer 11

thank you guys