Question 2. (15 pts) Let vi= (-3 0 6)", V2= (-2 2 317, V3= [0 -...

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Question

Answer 1

Answer #1

Q. 2. Let A = [v₁,v₂,v₃,w] =

To determine whether w is in the subspace spanned by v₁,v₂,v₃ and whether v₁,v₂,v₃ are linearly independent , we will reduce A to its RREF as under:

Multiply the 1st row by -1/3

Add -6 times the 1st row to the 3rd row

Multiply the 2nd row by 1/2

Add 1 times the 2nd row to the 3rd row

Multiply the 3rd row by 1/18

Add -7 times the 3rd row to the 2nd row

Add 1/3 times the 3rd row to the 1st row

Add -2/3 times the 2nd row to the 1st row

Then the RREF of A is

sThis implies that:

(1). w cannot be expressed as a linear combination of v₁,v₂,v₃ . Therefore, w is not in the subspace spanned by v₁,v₂,v₃ .

(2). The vectors v₁,v₂,v₃ are not linearly independent as v₃ = 2v₁-3v₂ so that 2v₁-3v₂ - v₃ = 0

Answer 2

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