a) Use the Gram-Schmidt process to transform {x1, x2, x3} into an orthogonal set {v1, v2, v3}. Use the order x1, x2, x3 given. (b) Using your answer from part (a), what is projx1,x2 (x3)? What is the error vector? (Hint: You can only use the projection formula on orthogonal vectors.) (c) Using your answer from parts (a) and (b), is x3 in Span{x1, x2}? Explain.

Q: Let A= 00 b) Say if A is diagonalisable sur Cv H E M3x3(C) such that H-¹AH is diagonal.

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Q: Suppose that r1(t) and r2(t) are vector-valued functions in 2-space. Explain why solving the…

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Q: 142 Q2. Let A = Determine a basis for each of the subspaces CS(A"), |3| 316 N(A), CS(A), and N(A").

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Q: Let u = (3, 2, x) and v = (2x, 4, x). (a) Find all possible values of x that make u and v…

A: Given thata)We have to find all possible values of x that make u and v orthogonal.b)We have to find…

Q: Show that A= 4 * eye (4) - ones (4, 4) is not invertible: Multiply A* ones (4, 1).

A: We have to show that:  A= 4 * eye (4) - ones (4, 4) is not invertible

Q: Find the cross product a * b. a=(4, 5, 0), b = (1, 0, 7) Verify that it is orthogonal to both a and…

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Q: *1. Which of the following are subspaces? Justify your answer in each case. (d) (x € R³ : x + x + x²…

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Q: 5. Let u= w= [-]-[], and w (a) Show that w is not a linear combination of u. (b) Show that u and V…

A: We have to show that-w is not a linear combination of u,u and v are linearly independent,w is a…

Q: I need help with this assignment. they all should have 4 places after the decimal place unless the…

A: Solution:

Q: If A is diagonalizable, show that A3 is also diagonalyable.

A: If A is a square matrix, then there is a non singular matrix P such that  is a diagonal matrix,i.e.…

Q: (2) Determine if the vectors are linear independent or linear dependent. Justify your answer. (a)…

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Q: Can we write v = (1,5,4) as a linear combination of u = (1,3, -2), uz = (2,7,-1), ug = (1,6,7) ?

A: If there exist a,b,c∈ℝ such that au1+bu2+cu3=v then we can say  v as a linear combination of u1,u2…

Q: o find the image of v and the preimage of w. , 2vq – v2 ), v = (1, 1), w = (-7/7, 2, -20) age of v…

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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/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: Use matrix multiplication to find the dilation of (a, b) with factor k = α, where α > 1

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Q: a) Find all the real numbers à such the vectors 1- x 1+x and x+1 1 are orthogonal.

A: Two vectors are said to be orthogonal if their dot product is zero. Dot Product There are two…

Q: Use the function to find the image of v and the preimage of w. T(V1, V2, V3) = (4v2-V1, 4v, + 5v2),…

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Q: Create x and y vectors to represent the following data: 10 23 20 45 30 60 40 82 50 111 60 140 70 167…

A: Que 1 Let the equation is y = a + b x + c x2 and solve the normal equation, obtained…

Q: Use the function to find the image of v and the preimage of w. T(V1, V2, V3) = (v2 V1, V1 + V2,…

A: Let us consider the transformation T: V→W defined as T(v)=w where v is preimage of w  and w is an…

Q: . Let W₁ -00--00 and W₂ = (b) 1 equal to (a) 0 be subspaces of R³. Then dim(W₁ W₂) is (c) 2 (d) 3

A: We have to solve given problems:

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: 4. Let P,(x) be the Lagrange interpolating polynomial for the data (0,0), (0.5, y), (1, 3) and (2,…

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