# Answer to Question #3204 in Linear Algebra for kalong08

Question #3204

Suppose x, y are elements of R^n and are nonparallel vectors.

a) Prove that if sx + ty = 0, then s = t = 0.

b) Prove that if ax + by = cx + dy, then a = c and b = d.

a) Prove that if sx + ty = 0, then s = t = 0.

b) Prove that if ax + by = cx + dy, then a = c and b = d.

Expert's answer

a) Prove that if s

If they are nonparallel than they can be chosen as the basis (orthogonal or not) in subset in

We have

∑(i=1 to 2) a

But these two vectors are linearly independent as they are two basis vectors and that mean that s = t = 0.

b) Prove that if a

We have

a

Supposing the same as we write before we get

a-c=0

b-d=0

a = c and b = d.

**x**+t**y**= 0, then s = t = 0.If they are nonparallel than they can be chosen as the basis (orthogonal or not) in subset in

**R**.^{n}We have

∑(i=1 to 2) a

_{i}**x**_{i}= s**x**+t**y**= 0.But these two vectors are linearly independent as they are two basis vectors and that mean that s = t = 0.

b) Prove that if a

**x**+ b**y**= c**x**+ d**y**, then a = c and b = d.We have

a

**x**+ b**y**= c**x**+ d**y**→ (a-c)**x**+ (b-d)**y**= 0.Supposing the same as we write before we get

a-c=0

b-d=0

a = c and b = d.

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