-5 15 -4 12 Let A = -3 9. 4 -12 Find k such that Nul(A) is a subspace of R* Find k such that Col(A) is a subspace of R* Let B = -3 -7 -5 4 Find k such that Row(B) is a subspace of IR Find k such that Nul(B) is a subspace of R* 9 1 0 10 2 Let C = 0 2 9 2 9 1 Find k such that Col(C) is a subspace of R* Find k such that Row(C) is a subspace of R*

Q: 7 4 -7 find the closest point to v in the subspace W spanned by 2 and 4 -2 Given i -32

A: The given problem is to find the closest point to vector v in the subspace W spanned by given…

Q: Let V₁ = -[---[- 3 the subspace W spanned by {V₁, V2, V3, V4). V2 and v₁ = [4] 9 Find a basis for

A: Row Reduce Echleon form

Q: A is a 8x6 matrix The nullspace of A is a subspace of R" where n = What is the largest the rank of A…

A: A is a 8×6 matrix We use Rank -Nullity Theorem If A is matrix m×n⇒rankA+nullityA=n

Q: give examples of subspace in R^2 and R^3 what can we say about the intersection of subspaces

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Q: (a) Let A = 2-4 -2 4 2-4 -36 Then: Null(A) is a subspace of R* where k = Col(A) is a subspace of R*…

A: According to guidelines , We solve only (a)

Q: Part II 1 2 3 The matrix A has rank A can be written as 2 4 6 A uv", where u and v = 2 00

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Q: Identify a basis for the following subspace: -a a-b W= W-[[ 26 42 D | ER₂10.0 ER} 4 2b 3a A ( 1 - ER…

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Q: Let A = 6 -9 12 -12 10 -15. Null(A) is a subspace of R*, where k = -2 3 -4 Let B = = [6 4 5 Col(A)…

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Q: Given 1 -8 -1 6 subspace W spanned by " find the closest point to in the 1 -4 - 2 1 and 2 –7 2 -26

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Q: Draw this figure to show the subspaces for A = [3²] & B = [38] Rn row space of A nullspace of A…

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Q: Q(2) determine whether the set W = {(a,a +b,b):a,b eR} is a subspace of R³. (2) Find th

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Q: Let M3,3 denote the vector space of all 3 × 3 matrices. Let L3,3 denote the set of all lower…

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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: Linear algebra

A: Consider the set

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: 4 11 5 -7 -97 0 1 4 11 5 -7 -97 6. is row equivalent to B= 5 -2 -4 2 4 3 3 3. If A= -1 1 find bases…

A: Given the matrix is A=4115-7-9-2-4246-107105-3-7028 which is equivalent to…

Q: For the subspace below, (a) find a basis for the subspace, and (b) state the dimension. F- s- 5t s+t…

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Q: Let L: R³ → R³ be the linear operator defined by L(x) = -1521 12x2 + 15x3 [25] -6x2 -45x₁ +45x3 (a)…

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Q: Recall that a subset V of R" is a subspace of two conditions hold: Condition (I): For all 7,7 in V…

A: Since V is a sub space of Rn, if  (i) V is closed under vector addition that mean sum of two vector…