(() 2 6. Are the two subspaces span and span (() orthogonal? Justify your answer.

Q: If S and T are subspaces of V, then SintersectionT is a subspace. Select one: True False

A: A detailed solution is given below.

Q: Is the set of all 2 x 2 matrices of the form a 1/ 1 b , where a and b may be any scalars, a vector…

A: The given set is a11b | a, b∈K. It is known that any subspace should contain the identity element.

Q: Determine whether the subspaces are orthogonal.

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Q: Why are [0,1] and (0,1] which are subspaces of the real number system with the usual topology not…

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Q: What is a linear subspace?

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Q: 10. Find a basis for the subspace spanned by the given vectors. What is the dimension of the…

A: Given vectors  1-32-4,-39-612,2-142,-45-37 we have to find    (a) Basis for the subspace spanned by…

Q: Show that (a,b,c) where c=a+b is subspace of R3

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Q: -2 3 Find the vector in the subspace W spanned by which is 1 27 closest to L 20] Answer:

A: *As this problem is related to Projection matrix, hope you know how to find inverse of a matrix,…

Q: Soal 1. 35. Find the closest point to y = (3,-1, 1, 11) in the subspace W spanned by V₁ = (1,-1,-1,…

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Q: -9 4 -3 -21 Find the vector in the subspace W spanned by which is closest to –1 -3 -5 Answer:

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Q: Q3 shew that W2 = subspace of R2 is a

A: To show any subset of vector space is a subspace , prove the following condition : Set is closed…

Q: 5а+ 2b Decide whether the set of all vectors of the form is a subspace of R³ or a

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Q: 1. Show that WW10 W2 is a vector subspace of V, but that W1 U W2 need not be a vector subspace in…

A: according to our guidelines we can answer only three subparts, or first question and rest can be…

Q: If S and T are subspaces of V, then SNT is a subspace. Select one: True False

A: Since this is a true or false question we can come directly into the solution without going into the…

Q: 3 1 Show that the null space of A is a 02 subspace of R³. Which subspace can you obtain by the…

A: It is given that,  A = 13-1024 We have to show that the null space of A is a subspace of ℝ3 and to…

Q: Why isn't R2 a subspace of R³?

A: For being a subspace a space must be a subset of the other. But here R2 is not a subset of R3. So…

Q: ) Find a linearly independent set of vectors that spans the same subspace of R' as that spanned by…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 6. (a) Determine whether the set of all vectors of the form (a,b,c), where b a+c, is a subspace of…

A: The subspace of R3 is (a,b,c) where b=a+c

Q: Verify that V5 is a subspace of RS

A: Please check step 2 for solution.!

Q: very vector of subspace W5 is orthogonal to each vector in subspace V5.

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Q: Discuss what it means to be a subspace and what is required to prove that something is a subspace.…

A: Concept:

Q: (3) (a) Prove that if two linear subspaces are orthogonal, their intersection consists of only the…

A: (a). Prove that if two linear subspaces are orthogonal, their intersection consists of only the zero…

Q: 1 for which x value span the vector subspace? -1 13 - 2 -1 O A) 2 в) .1 O C) 0 D) 1 O E) -2

A: We have to find x

Q: 3 5 2 and find the closest point to i in the subspace W spanned by -5 Given i -6 3

A: Givenv→=34-55and let s1→=52-61 and s2→=0734The formula of orthogonal projection of v onto span of s1…

Q: 7. The vector i = is in a subspace II with hasis B- 32 Find the B-coordinate vector of

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Q: 2 7 -6 find the closest point to v in the subspace W spanned by -4 9. Given v = -2 and 2 -9 -18

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Q: (a) If a 7 by 9 matrix has rank 5, what are the dimensions of the four subspaces? What is the sum of…

A: Use the given information.

Q: How do you find a basis for a given subspace? May you please throw in an example too?

A: See the attachment.

Q: Find a linearly independent set of vectors that spans the same subspace of R' as that spanned by the…

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Q: Let P2 be the vector space of all polynomials of degree 2 or less, and let H be the subspace spanned…

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Q: Give an example of a two-dimensional subspace of R4 .

A: Consider two-dimensional subspace of R4 is, u1=1111, u2=110-2

Q: 8) Describe geometrically all subspaces of R" for n 1, 2, 3.

A: We will do this for all three parts; n = 1, 2, and 3 (in as clear handwriting as possible)

Q: pan(1,1 – x, 1 +x², 2x – 3) = span(2, 2 – x°, 2x² – x, x + 1). - %3D - -

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Q: 2 2 , find the closest point to v in the subspace W spanned by 6 and 3 Given i = 6. 1 12

A: To find  The closest point to V in the subspace spaneed by the given vectors.

Q: Find a linearly independent set of vectors that spans the same subspace of R' as that spanned by the…

A: 1.  Form a matrix using the vectors of the subspace as row vectors and row reduce the matrix using…

Q: If X = {a, b, c} and 1 = {X, 4, {a}}. Then the subspace topo log y on A = {b} is {Ø, {a, b}} {Ø,…

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Q: a a + b 2a – b Show that the set of vectors of the form forms a subspace of basis for this space.…

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Q: a + 2b a + 1 3. Is H = a subspace of R? Why or why not? a

A: We need to determine if H=a+2ba+1a is a subspace of ℝ3 For a set W to be a subspace of a vector…

Q: Define Vector Space and Vector subspace with the help of real time examples?

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Q: 3.4. Find the distance from a vector (2,3, 1)" to the subspace spanned by the vectors (1, 2, 3)",…

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Q: What is the dimension of the subspace 0 2 3 1 H = x1 x2 x3 X4 ER¹ : 2x1 3x2 + 4x3 5x4 = 0 ?

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Q: 1. Determine whether the set W =- ER,x, is a subspace of R' with the standard operations. Justify…

A: Given the set W=x1, 1x1, x3 | x1, x3∈R, x1≠0 We have to determine whether W is a subspace of R3with…

Q: 1 3 6. (4) (a) Find orthonormal vectors ĝ1, 2 in the subspace Span{a, b} spanned by ä = 7 of R5. 1…

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Q: I am having troubles understanding intersection of subspaces. For instance, I have these two…

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Q: Why are [0,∞) and (0,∞) which are subspaces of the real number system with the usual topology not…

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Q: [x++2x2 -X1 :X1, X2 real numbers is a subspace of R4 with dimension dim H H = 3x1-X2 X1+X2

A: I jave used that dimension of a space is equal to cardinality of basis And found a basis of H which…

Q: Consider the system of equations on R2 y – 4a3. . Find stable and unstable subspaces.

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Q: Determine whether the subspaces are orthogonal.

A: Given,  S1=span1,1,1,1S2=span-1,1,-1,1,0,2,-2,0

Q: da basis of the subspace of IR* defined by the equation 5x1 + 9x2 + 8x3 + 6x4 = 0.

A: Explanation of the solution is given below...