a. The zero vector 0 is in ker(A) b. If x and y are in ker(A), then so is z = x + y. c. If x is in ker(A), then so is z = cx where c is a scalar.

Q: Let ^= [1] -6 Find a unit vector x whose first component is positive at which Ax has maximum length.…

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Q: Let P(4, 3, –1) and Q(6, – 1,3) be two points in three-dimensional space. (a) Find the distance…

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Q: Determine the vector fald of . Fa, -- %23

A: The given vector field is                                            V(x,y)=4i-2j

Q: 1. Let, p is the set of all vectors of the form: m,n, te R. 2n (a) Is p closed under vector…

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Q: Let P = (4, 1, a), Q = (-2, 0, b) and v=i − 3j + 4k be two points and a vector in R³ respectively.…

A: The given points are 4,1,a and -2,0,b. The given vector is v=i-3j+4k in ℝ3.   The vector equation of…

Q: If T is defined by T(x) = Ax, find a vector x whose image under T is b, and determine whether x is…

A: Her we solve the linear equation to get the solution.

Q: let A = [1 5 -4 -3 0] and w = [1]            [0 1 -2  1  0]              [2]            [0 0  0   0…

A: Answer is in below steps.

Q: (a) Suppose A=(S,+S) and B (S-S), Show that S = A + B A= A and B =-B (b) Suppose that A B, is a…

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Q: Consider the 4-vectors Aª = (a, 0, 2a, 0) and Bª = (23, 0, 0, 0), where a and 3 are non-zero real…

A: and .It is given that  is null vector.

Q: 3- The scalar component of the vector F in the direction of K is (K.F А- .K, В- K C-

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Q: E Let z = 1+ i and z'=i-1. 1) Are these two complex numbers independant in the real vector space C?

A: We checked two complex numbers independant in the real vector space C?

Q: Let 1 0 1 2 3 3 A = -( : )--( * = 0 1 1 02 B = 0 1 1 02 ● 000 00 0 0 1 0 1 Which of the following…

A: Solution:

Q: Let u and v be vectors and c be a scalar. Select the best statement. A. c(u + v) = u + cv O B. We…

A: Given Let u and v are the two vectors c is a constant

Q: 2 3 [+0 4 2 b = -2 Select true or false for each statement. Let A = and c = [12] 1. The vector c is…

A: The objective of the question is to determine whether the given vectors b and c are in the kernel…

Q: 2. (а) ở and w are vectors in R? such that f(0) = w. Express f(27 – 3w) as a linear combination of i…

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Q: The vectors T and N, when defined, (a) are parallel. (b) are orthogonal. (c) have a zero cross…

A: T is the tangent vector and N is the normal vector.  So they are always orthogonal to each other.

Q: If T is defined by T(x) = Ax, find a vector x whose image under T is b, and determine whether x is…

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Q: true or false prove your answer If (an) is Cauchy and p is a number such that for infinitely many…

A: Given that              an is a Cauchy sequence and p is a number such that for infinitely many…

Q: Let A = - 7 -6, b 3 2 = [4].. and c = Select true or false for each statement. [1] 1. The vector c…

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Q: 7.8 Prove, by writing it out in component form, that (a × b) × c = (ac)b — (b. c)a, and deduce the…

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Q: Let ū = -4î + 4ĵ – 3k and i = î – 25 + 2k. (a) Let w = proj, ū. Compute w. (b) Compute u-w and show…

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Q: Calculate the scalar triple product, (ux v). w, ofu, v, and w where u = -141-43, v = 10i-20 + 15k,…

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Q: Show that the complex numbers 2 + 3i and 1 – 2i generate the vector space

A: Given complex numbers are z1=2+3i    and    z2 =1-2i and   given vector space  is   ℂ over ℝ

Q: (3) Let L be the line y 2r in the plane. Find a matrix C such hat for every vector H plane, the…

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Q: the following. 1 1 1 A = B = 1 -1 1 3 b be scalars. Find aA + bB. e whether C is in span(A, B). in…

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Q: Using index notation, prove the following identities among vectors A, B, C, and D: (a) (A x B). (B ×…

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Q: 4. Find the scalar and vector projections of b onto a (a) a =, b = (b) a =, 6=

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Q: 4. In the vector space P3(R), let S = {p1(x), p2(x), p3(x)}, where P1 (x) = 63x° + 19x² – 37x – 41,…

A: (a) we see, p2(x) = -3p1(x), so S is not linearly independent. [Ans] (b) As S is not linearly…