Let A = Then a) A is unitarily diagonalizable and can be factored as

Q: Given that p and r find in column vector form:

A: In this question, we find the column vector by using the given vectors.

Q: If AB = 0, the columns of B are in the nullspace of A. If those vectors are in R”, prove that…

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Q: AB is orthogonal

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Q: (a) Prove that u + vand u - v are orthogonal in IR" if and only if ||u|| = ||v||. (b) Draw a diagram…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Let x, y, and z be vectors in Cn and let a and B be complex scalars. Show that a ( z, x) +B ( z,y )…

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Q: Prove that if A is invertible and diagonalizable, then A-1 is also diagonalizable.

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Q: e diagonalizable?

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Q: In each part, determine whether the vectors are linearly independent or are linearly dependent in…

A: We have to find the given vectors are linearly independent or dependent  Here year I am solving…

Q: Find the orthogonal complement to the row space of A and its dimen- sion.

A: Given , A = 125213037 Then , the now-space is span of                   (1,2,5)  ,  (2,1,3)  and…

Q: C. If a =.Find a vector b such that compab = v2. %3D

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Q: 1. Calculate the area of the parallelogram spanned by the vectors Á = and B = .

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Q: Find the norm of a and the unit vector u in the direction of if 1 3 x = ||*|| = 13 = = 81 -4 Y ♡

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Q: suppose M is the set of all real column vectors R4 whose components are equal , then the basis for M…

A: suppose M is the set of all real column vectors R4 whose components are equal , then the basis for M…

Q: find all the scalars k such that || kv || = 3, Where v = (-1, 2, 0, 3)

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Q: |A student writes the statement ā.b = b.č and then concludes that a = č. Construct a simple…

A: The given problem is related to vectors. Given: a student writes the statement a→ . b→ = b→ . c→ and…

Q: (2) Prove that if a + b and a – b are orthogonal, then a and b have the same magnitude.

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Q: Find the norm of a and the unit vector u in the direction of a if -5 -4 1 ||#| = u = || 18 ||

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Q: If Lo and Li are parallel, then vo = is a scalar multiple of vi = . اختر احدى الدجابات

A: If two lines  L0: (x,yz)=(x0+a0t, y0+b0t, z0+c0t)And,L1:(x,y,z)=(x1+ sa1, y1+sb1, z1+sc1) Are are…

Q: For each matrix A in Exercises 14 through 16, find vectors that span the image of A. Give as few…

A: 15. Given,             A=11111234

Q: Prove that if a square complex matrix is unitarily diagonalizable, then it must be normal.

A: Every square complex unitarily diagonalizable matrix is normal. Let, A be a square complex unitarily…

Q: a) Prove that ||u + v|| = ||u - v|| if and only if u and v are orthogonal, (b) Draw a diagram…

A: a) Suppose u,v are orthogonal. Now…

Q: When V is spanned by {v1, v2, . . . , vk} and one of these vectors can be written as a linear…

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Q: Assume that th e product AB makes sense Prove that if the columns of B are linearly dependent, then…

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Q: Show that if v and w lie in the yz-plane, then v × w is a multipleof i.

A: Both vectors v and w lie in the y-z plane, which means they must have zero magnitude component along…

Q: snip

A: Given Orthogonally diagonalize A=abba,If b not equal to zero

Q: Find the norm of i and the unit vector i in the direction of a if ||7|| =

A: Solutions

Q: . Prove that (only one): E - 4y-V3ay is a unit vector? a- F 2 b- A = 6ax - 3a, + 2a, and B = 3a, +…

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Q: If d is a scalar multiple of b, then ax%. Select one: True False

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Q: Prove that, if A is similar to B, and B is diagonalizable, then A is diagonalizable.

A: Given that A is similar to B and B is diagonalizable.  To find A is diagonalizable.

Q: If the column space of A is C(A) = R", then det A +0. %3D O a. TRUE O b. FALSE

A: The solution are next step

Q: Exercise 9.9 A. 1. ABCD is a square. The diagonals intersect at O. FB. AE Prove that EO = FO. %3D B.…

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: Show that if Aij is symmetric and Bij is skew-symmetric, then the scalar η given by η = AijBij is…

A: A tensor aij is said to be  symmetric if aij=aji. Similarly a tensor bij is said to be anti…

Q: Suppose that A is a square matrix and that ∥Au∥ = 1 for all unit vectors u. Show that A is…

A: Given: To show that A is orthogonal, assuming that A is a square matrix. Here Au =1for all unit…

Q: Find a basis for the space spanned by the given vectors, vl.,., v5. [M]

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Q: Sketch the following Cartesian products on an x, y-plane. (2) {2, 4, 6} × {0, 1, 2} (b) [0, 2) x {1,…

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Q: Prove that |A|B + |B|A is orthogonal to |A|B – |B|A, for any vectors A and B.

A: We need to show that |A|B + |B|A is orthogonal to |A|B – |B|A, for any vectors A and B. Here, |A|…

Q: Prove that if A is not square, then either the row vectors of A or the column vectors of A form a…

A: Suppose A is an x×y matrix that is not square. Either A has more rows than column (x>y) or more…

Q: Prove that  A + At is symmetric for any square matrix A.

A: Known facts:

Q: Is Vector Y in the Column space of A? What is the solution set? Write y as an appropriate linear…

A: the vector y is in the column space of A is the system Ax=y is consistent 819-59-13108abc=123…

Q: snip

A: Assume that the set 123,  41-2,  ab3 is an orthogonal. This implies that, a, b, 3·1, 2,…

Q: Let A = Show that A can be diagonalised. Then, compute A°.

A: The solution of the problem is given in the next steps.

Q: Determine m such that the two vectors are orthogonal.

A: Given : 3i-2j and 4i+5mj

Q: Find scalars s and t so that LU = A.

A: Given: A=2611, L=20t-2 and U=130s. To find scalars s and t so that LU=A. Solution: Finding LU.…

Q: Find a nonzero column vector u such that Cu = 4u.

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Q: Let TilPe > Pz , T (ax?+bx+c) = 2Qx+ b. Then the basis of NIT) is

A: Just use a definition of Nullity of transformation.

Q: If A has two orthogonal columns each of length 6. Then A^TA is equal to

A: See the attachment

Q: s such that vectors –si – 2j+5sk and 9si +j+3sk are orthogonal.

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Q: Show that the vectors a = 3i−j+4k, b = i−3j−2k and c = 4i−3j+2k are linearly independent. Find…

A: Show that the vectors a = 3i−j+4k, b = i−3j−2k and c = 4i−3j+2k are linearlyindependent. Find…