Linear algebra

username6035217

I don’t understand this rule and have no idea where the 3 and -2 came from?

(edited 11 months ago)

Reply 1

mqb2766

Original post by Stress2638,,,

I don’t understand this rule and have no idea where the 3 and -2 came from?

Theyre just arbitrary scalars to show that v is a linear combination of the basis vectors u1 and u2. Its a bit like saying a line is
y = 2x + 3
the 2 and 3 are just arbitrary scalars

(edited 11 months ago)

Reply 2

username6035217

Ohhh okay that makes sense, thanks :smile:

Original post by mqb2766

Theyre just arbitrary scalars to show that v is a linear combination of the basis vectors u1 and u2. Its a bit like saying a line is
y = 2x + 3
the 2 and 3 are just arbitrary scalars

Reply 3

username6035217

Original post by mqb2766

Theyre just arbitrary scalars to show that v is a linear combination of the basis vectors u1 and u2. Its a bit like saying a line is
y = 2x + 3
the 2 and 3 are just arbitrary scalars

What about for this example? How do you know it’s not a linear combination?

Reply 4

mqb2766

Original post by Stress2638,,,

What about for this example? How do you know it’s not a linear combination?

u2 is simply a scaling of u1 (multiplied by 2), so any linear combination of u1 and u2 is also simply a scaling of u1. Here v is obviously not a scaling of u1.

(edited 11 months ago)

Reply 5

Muttley79

Original post by Stress2638,,,

What about for this example? How do you know it’s not a linear combination?

You need to show that a multiple of the first + mutiple of the second cannot give that answer.

Reply 6

username6035217

Original post by mqb2766

u2 is simply a scaling of u1 (multiplied by 2), so any linear combination of u1 and u2 is also simply a scaling of u1. Here v is obviously not a scaling of u1.