Let ū = -4î + 4ĵ – 3k and i = î – 25 + 2k. (a) Let w = proj, ū. Compute w. (b) Compute u-w and show that u- w is orthogonal to w.

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Q: Find the conjugate of z = u+w If u = 6+2i,z= 1+4i

A: Step 1: The conjugate of a complex number z=a+bi is: zˉ=a−bi i.e., it is obtained by changing the…

Q: Calculate the scalar triple product u (vx w), where u = . (Use symbolic notation and fractions where…

A: Here we have to evaluate the scalar triple product u. (v x w) .

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A: We have to find out

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A: Introduction:  The vector projection of a vector a on (or onto) a nonzero vector b, sometimes…

Q: let u = 2i -5j  ;   v =-3i+7j  ;    w=-i-6j Find each specified vector of scalar A. 3w+2v b.…

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Q: Let y = and u = Write y as the sum of two orthogonal vectors, y, in the span of u, and y, which is…

A: Solution

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: -54 ) Express the vector i and y -5 as a linear combination of a = 4 y.

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Q: }] respectively. Let y = and u = . Write y as the sum of two orthogonal vectors, y, in the span of…

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A: Projection of vector u on vector v is given by  Projv(u) = u.vv2 v Here u = -i+5j+3kv = -i+j-3k…

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Q: Multiply the matrix P = A(ATA)-¹AT by itself. Cancel to prove that P² = P. Explain why P(Pb) always…

A: Here the Matrix . For this matrix P, .

Q: 4. a) b) Let x = 27 + 3j - k, y = i- j + 4k and Z = −3ỉ + ]. Express the vector x – ỷ – 3ž in terms…

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

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A: The linear map G maps  to the parallelogram in XY-plane.The parallelogram is spanned by the vectors…

Q: X b) Let T 10 Find the Kernel of T. Write down the range of T as a span of independent 5x vectors.…

A: Obtain Kernel of T as follows.

Q: v1 =[ 2 5 1 ] , v2 =[ − 3 1 − 1 ] , b =[ 11 19 5 ] Show that b is in Span{v1,v2}. Express b as a…

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