3) Let B, = {u,, u2} and B2 = {v,, v3} be the bases for R° in which u, = (1,2), uz= (2, 3), v = (1,3) and vz = (1,4). Let w = (3, –3). Find [w]B, and then use the matrix PB,--B, to compute [w]B, from [w]B, -

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A: We know every lower or upper traingular matrix is a triangular matrix.

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Q: (i, 2, 3i), v = Co over C. Are these vectors linearly independent? Can they form a basis 5.…

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Q: Find out Vector S= { V, V2, V3} is the Basis por R. if VI : ( 3,1,-4), Vz C2,s,6), V3 - C1,4,8) %3D…

A: Here we have to find whether v1 , v2 , v3 are basis of R3 or  not.

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A:

Q: Consider four row vectors u, u, w, z of size 1 x n each and let a, bER Then. by multilinearity of…

A: The given statement is

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A: Given u, v=-3v1u1-3v2u2 u=-3-2, v=14

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A: first draw a figure as below

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A: See the detailed solution below.

Q: Now assume that f and g are both C2. Express the matrix of second derivatives V²F(x) in terms of f…

A: b)

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Q: 1. Let A = [a;j]4x5, B = [bij]4x5; C = [cij]5x2; D = [d:j]4x2, and E which of the following matrix…

A: Matrix addition: Let A be an m×n matrix and B be an also m×n matrix. A= {aij: 1≤i≤m ; 1≤j≤n} and B=…

Q: orthonormal 3D vectors

A:

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A: Prove.

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Q: Let x1,...,xk be linearly independent vectors in Rn, and let A be a nonsingular n×n matrix. Define yi…

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A: Consider the given: w=010011011

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A: Given statement is true.

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A: Given:Let r1.......rp be vectors in ℝnLet Q be an m×n matrix Qr1.......QrpR=r1.......rpQ=Q…

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Q: Let v = 2i + 4j and w = -2i + 6j. Decompose v into two vectors, v1 and v2, where v1 is parallel to w…

A: v=2i+4j  &  w=-2i+6j Now, v·w=2-2+46=20 & w=-22+62=40 Now,…

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Q: the norms of a vector X = [1,12, ...,I" and matrix A = (a5) are respectively defined as ||X|| = E…

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Q: If u = (3, −1, 4) and v = (−2, 3, 5), the scalar projection of y onto v is:

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Q: If P is the projection matrix onto the line through () -- (;) C) and ) then I – P projects onto the…

A: I have checked one by one option wise

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Q: i) Find the matrix of T with respect to ordered basis B' = {(1, 1), (1, – 1)} %3|

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Q: +0, then the matrix H = I – 2- vv7 is orthogonal and symmetric. Show that if the vector v

A: Given  H=I-2vvTvTv

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A: Let's suppose we have a linear relation:…

Q: Write x as the sum of two vectors, one in Span fu,,u2,U3} and one in Span fu4). Assume that fu. 44…

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A: This is a problem of vector calculus.