(3) Is Mmxn(Q) is a vector subspace of Mmxn (R) over R?

Q: A vector y in Rn can also be viewed as an n × 1matrix Y = (y). Show that ||Y||2 = ||y||2

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Q: Is the set of all vectors (x, y) in R, with the usual addition and scalar multiplication, a subspace…

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Q: The vector x is in a subspace H with a basis ß = {b1,b2}. Find the ß-coordinate vector of x. b₁ =…

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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: I) Show that W = {(a, b,a-b): a, b e R) is a subspace of R³ and find its dimension.

A: W = {(a, b, a - b) : a, b ∈ R} Clearly, W is a subset of R3.     Let, (a1, b1, a1 - b1), (a2, b2, a2…

Q: R? Which vector stretches the x + y = 0 subspace of ? Why is that? a. (2,1) b. (0,0) c.(1, -1)…

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Q: . Consider M₂ (R) as a vector space and its subspaces U₁= {A € M₂(R): A¹ = A} and U₂ = {A € M₂(R) :…

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Q: Let W be a subset of the vectors in R where W = X2 X4 -x3 = x, - x, }. Show that W is a X3 3. X4…

A: We will use the formal definition of a subspace of a vector space to prove that, W is a subspace of…

Q: b) Is W = {f(x):f is a polynomial with degree <3,f (0) 0} a subspace of P: all 3 ? Explain your…

A: To see if the given subset is a subspace of the vector space of all polynomials of degree less than…

Q: When multiplying a scalar and a vector: |xa|=A|ā| when A |xa|=|||ā| when X + 0 and ◆ 0.

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Q: Determine the following is the subspace in R’? W ={(x,y,z):x+y+z=0}

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Q: c) Show that vector ū = 1 cannot be expressed as a linear combination of 2 in R3 3 vectors vi 1 and…

A: we have to show that , we can not write as a linear combination of vectors v1 and v2

Q: 1 (b) Find the span of vectors i = |0 and j = |1 in R3

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Q: АT (Ь — Ах) — ӧ. Interpret this statement in terms of the fundamental subspaces of A.

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Q: True or False, S is a subspace of R 3 x1 (8] x2 x3 S = O True O False 2x1 + x3 = 0, x1 + x2 = x3 = 0…

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Q: True/False: If V is a subspace of R", then dim(V) + dim(V+) = n. True False

A: This is true and follows from a famous theorem in linear algebra.

Q: 3. Find a parametrization for (a vector valued function that traces) the line which passes through P…

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Q: 2t 6. Let H be the set of all vectors Show that H is a subspace of R³. What is the -t dimension of…

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Q: Find the coordinate vector of v = with respect to the basis -000 1 for the subspace of R4 spanned by…

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Q: Let $K$ is a horizontal shear, next draw a vector $\vec{x}=\left[\begin{array}{l}x_1 \\…

A: Let be the transfomation representing vertical shear of the vector  .Then we have The above can be…

Q: (1) Is Mmxn(R) a vector space over the rational numbers Q? Explain. (2) Is Mmxn(Q) is a vector space…

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Q: Be F1(x, x, x) e R³ and F2(a, b,0) e R³ a)show that F1 and F2 are subspaces of R3 b)show that R' =…

A: Solution of the problem as follows

Q: Use the function to find the image of v and the preimage of w. T(V1, v2) = (Vị + v2, V1 - V2), v =…

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Q: Find a vector-valued function whose graph is the plane x+y+z= 12, O r(u, v)=-ui-vj+(12-u-v)k O r(u,…

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Q: 2

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Q: 3) Find a basis for the subspace of R that consists of the intersection of the planes X-3Y = 5Z and…

A: This is a problem of vector space.

Q: Use the function to find the image of v and the preimage of w. T(V₁ V₂ V3) = (4V₂ - V₁₁ 4V₁ +5V₂), v…

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Q: 3. Suppose W (a) (b) a = = {( 2 ): 9₂ Prove that W is a subspace of M2x2 (R). : a, b, c ER CER}.…

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Q: (b) Find two orthonormal vectors u₁, u₂ that span the same subspace of R³ as V₁ = [3,4,0]¹, V₂ =…

A: Here given vectors v1=340, v2=213