5.7 Show that a line in IR³ that does not pass through the origin cannot be a subspace of IR³.

Q: Find a basis of the subspace of IR" defined by the equation 8ar1 - 7z2-4r3 0. { Basis:

A:

Q: Find an orthogonal basis for the subspace Span (1, 1 + x, 1 + x²) ≤ P3. Justify your answer!

A: Using the Gram Schmidt orthogonalisation process:

Q: Find the dimension of the subspace spanned by the given vectors: u₁ = (1, 3, -2,5), u₂ = (0, 1,-1,…

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Q: The matrix that projects onto the x-y plane is

A: We have to find the matrix that project onto  plane

Q: Let B Let v = x1 || 2 {]-G]} 3 13 15 then 8 0 be a basis for the subspace H. X1 where " x2 X2

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Q: 19. Prove that the set of all vectors in R³that satisfy the equation x₁ = 3x2, is a subspace.

A: (.)  Let set  'S'  is given by ,        S=x1,x2,x3∈ℝ3  :  x1=3x2 or   S= x1,x2,x3∈ℝ3 :  x1-3x2=0…

Q: 4. Find a basis and the dimension of the subspace W of V = M22(R) spanned by %3D -5 2 -4 A = B = C =…

A: Given:          V = M2 × 2(ℝ) spanned by A = 1-5-42 ; B = 11-15 ; C = 2-4-57 and D = 1-7-51   To…

Q: -10 2 -+-+- = -3 8 ) Given : -5 B-B and -4 6 -34 find the closest point to in the subspace W spanned…

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Q: Let V₁ = V₁ and v2. 1 -4 , V2' = -2 3 and w= -3 Determine if w is in the subspace of R³ generated by…

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Q: Show that [0,1] and (0,1] as subspaces of R with the usual topology are not homeomorphic.

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Q: Find a basis of the subspace of IR defined by the equation 871 - 7x2 - 4x3 = 0. Basis:

A: