4) Suppose u, v E V, where V is an inner product space, and ||u|| = |||| = 1 and (u, v) = 1. Find u - v. 5) Suppose U and W are finite-dimensional subspaces of the inner product space V, with W CU+. Find Py Py. %3D

Q: Prove thatII = {(x, y, z)|x – 2y+ 3z = 0}is a subspace of JR³, %3D -

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Q: Let W = {a + bx + cx2 + dx c- 3d = 0} be a subspace of Pg. Then th dimension of W is equal to %3D O…

A: ANSWER :

Q: Suppose U, W,, W, are subspaces of a vector space V. Show that (Un W,) + (UnW,)Cun (W, + W,) Find…

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Q: In the vector space , with the Euclidean inner product (i.e. the dot product), consider the subspace…

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Q: 4) Show that the subspaces of R? are precisely {0}, R2, and all lines in R? through the origin.

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Q: (b) If V = R", and U is a subspace of V of dimension m with 0 <m <n, prove that U² = {v € V: B(u, v)…

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Q: 4. Decide if the following statement is True or False: Let U, W, and X be subspaces of a finite…

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Q: show thal the set of all poiuts in the Subspace of IR 3. plane ax +by+CZ =0 is +cz = ois CA

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Q: #Consider the vector space R' (over R) and ZcR consisting of vectos z=(2,2, 2,), with these…

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Q: Find the orthogonal projection of 3 onto the subspace W of R* spanned by 1 -1 -1 projw (7) = %3|

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Q: Suppose U1,U;, -..Um are finite-dimensional subspaces of V. Prove that U + Uz + .. +Um is…

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Q: Let W = (a + bx + cx² + dx*lc- 3d = 0}be a subspace of Py. Then the dimension of W is equal to None…

A: To find - Let W = a + bx + cx2 + dx3| c - 3d = 0 be a subspace of P3. Then the dimension of W is…

Q: Consider the following subspaces of R3: U=span[(2, 1, 1), (1, 2, 0)] W=span[(0, 2, 1), (0, 1, 2)]…

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Q: If u and v are vectors in R and W is a subspace of R with (u - v) belong to W, then both u and v…

A: If u and v are vectors in R3 and W is a subspace of R3 with (u-v) belong to W, then both u and v…

Q: Suppose W,, W2,. (a) span (W, W2 (b) If S; spans W; for i = 1,...,r, then S, US, U...US, spans W, +…

A: (a) W1+W2W1+W2 would be W2W2. Below is the justification.  x+y∈W1+W2,wx+y∈W1+W2where x∈W1x∈W1 and…

Q: 9. Find the orthogonal projection y of y = onto the subspace 2 0. W Span u = -3

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Q: 6. Show that the closure Ỹ of a subspace Y of a normed space X is again a vector subspace.

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Q: , dim W 5. Let U, W be subspaces of a vector space V. If dim U and Un W = {0}, what is dim (U+ W)?

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Q: 16 In the vector space R, let u= (1, 2, 3), v -(3, 1, 5), w-(3,-4, 7). Prove that the subspace S…

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Q: Find the orthogonal projection of 4 onto the subspace W of IR' spanned by 1 1 -1 1 1 1 1 projw (7)…

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Q: the set B=E[f る,L 2 ), L3 10 in M22 the subspace of Mez spanned by B. Since carly independent Cyou…

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Q: If X a normed space and y is a proper proper Linear subspace of X. show that y has empty interior.

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Q: 3 show that if w is a subspace of fini a dimensional vector space y and dim (W) = dim (V) W = V.

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Q: 2 Find the orthogonal projection ŷ of y = onto the subspace 3 -2 W = Span { ui u2 Ex: 1.23 ŷ =

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Q: .a. Is the set of vectors W = {(x,y,z) x,y,z € R,x=z+2} subspace of R³?

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Q: if a vector space is the set of real valued continuous functions over R , then show that the set W…

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Q: 16 In the vector space R, let u= (1, 2, 3), v = (3, 1, 5). w = (3,-4, 7). Prove that the subspace S…

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Q: 4. Prove or disprove that the set of unit 2 vectors of R2 is a subspace of R2under usual operations

A: solve the following

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Q: Q.4 Show that U {(x, -x) |x in R} is a subspace of R?. %3D

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Q: Consider X = {1, 2, 3, 4, 5} where the topology is {UC X|1 € U}. Find a subspace of X which is…

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Q: Verify that if W is a subspace of an inner product space Vand v is in V, then perpw(v) is orthogonal…

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Q: Denote by C[0, 1] , the space of all continuous functions defined on the unit interval [0, 1]. Show…

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Q: a) Prove that W = {(a,b, 2a + b)} is a subspace of R. (more space on the next %3D if needed)

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Q: 1 SROW thet w in not a subspace 3 a Vecíor space V=R, where wis defined

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Q: 4. Find the distance from the vector j = to the subspace on R³ spanned by { 19: | }

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Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.