a) [The set v = U2 U1- - V2. [2].110 b) a basis for R². The set S = If v E span{v₁, U₂}, then U = ◆ 3 4 [8].0₁ = [2]. U1 c) The set S = span R2. {0.4} {[5].[B]-[]} +

Q: Let →a=a→= and →b=b→=. Find kk so that →aa→ and →bb→ will be orthogonal (form a 90 degree angle).…

A: We Know that, Two vectors u and v are said to be orthogonal vectors if and only if u . v=0 Here, a =…

Q: Given that {an, 92, 93, any is a linearly independent set of vectors in a Vector space • V'( note…

A:

Q: Let u = (3, 5, -7) and v = (6, -5, 1). Evaluate u + v and 3u - v.

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Q: Q) Let û = 2745, Vz+3 , and w=T-5 find Scalars a and b such that u - av + bw

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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: Suppose that {x1, x2, x3} is a linearly independent set of vectors in a vector space V . Must {x1,…

A:

Q: Let B={(1,-2,1), (4,-7,5), (5,-8,8)], and x=(-6,10,-7) Find [x]B

A:

Q: Evaluate ( 3+j4)( 3+j4) = A +jB, determine the real component A

A: Given,              (3+j4)(3+j4)=A+jB

Q: -1 -2 -3 -41 1 2 3 Let A = 1 2.) Find adj (A)

A:

Q: Suppose that u, v, and w are vectors in an inner product space such that (u, v) 1, (u, w) = :8, (v,…

A:

Q: 5. Show that the set of complex numbers can be considered a vector space over the set of real…

A: A Complex number is in the form x + yi where x , y are real numbers and i is an imaginary number.…

Q: Let u = (5,-5, -7) and 7 = (-6, 1, 2). Compute the following: úxv= v X ū= úxu 3 (u xv) = ū × (30) =…

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Q: Q2. Let a vector A = [8-463] a) Compute the square of each element. b) Compute the square root of…

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Q: 8.) Find a vectorx such that 5x-2v=2(u-5x) SOLUTION

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Q: 5. For ea three c and be a)

A: Note- Since you have posted a question with multiple sub-parts, we will solve first three sub-parts…

Q: Let u = = (–3, 3, 5) and v = (−6, −4, −7). Compute the following: ū X x v = v × x ū x ū ū=

A: Please note that as per bartleby guidelines, we need to answer only the first three sub-parts.Kindly…

Q: Let u = (2, -1,3), v = (3,0,1) and w = (-1,-1,3). find all values of I, m and n such that lu + mv +…

A:

Q: valuate a.j8 1 b.- ¡7

A: Note- Since you have asked multiple questions, we will solve the first question for you. If you want…

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: Let x(bar) = (3,-5,2,1,-2) element of R5. Find the norm of x(bar) using the usual norm on R5

A: The norm of x is the distance between a point x to the origin.

Q: Q) Let A be diagonalizable so that P-1AP = D. Show that A2 must be diagonalizable.

A:

Q: 3. Find all real numbers t for V = (20 t,4t - 4,5t², t²) are orthogonal. - which = (1,5t,-4t, t³)…

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Q: = If w₁, W2, W3 are independent vectors, are the sums V₁ = W2+W3 and V₂ W₁ +W2 independent or…

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Q: Find |A|, [B], A + B, and JA + BỊ. Then verify that |A| + |B| = |A + BỊ. 1 7 A = 1 -1 0 0 1 -1 B = 7…

A: We can solve this as follows:

Q: Let X₁ = [1 3 −1 1]²‚×₂ = [3 −1 3 1]′, and x3 = [-1 2 −3 1]. Is b = T an element of span{X₁, X₂,…

A: No, we can write it.

Q: For any two vectors ā and 5, show that (1+laf)(1+|5)=|1-a5f +a+5+āxbf.

A: Explained below

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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Q: a + b+c a + 26 + 4c + 2d` 3. Let m(a, b, c, d) = and set (а+ 2b + 3с + d a+ 2b+ 3c+ 2d) {m(a, b, c,…

A: We have to determine the dimension of the subspace M of M2(R) .

Q: Let u= (1, 8i), v = (7i, 7 + i), w = (1 + i, 0), and k = -i. Evaluate the expressions in parts (a)…

A:

Q: Describe the solutions of x1 + 2x2 – 3x3 = 5, 2x1 + x2 – 3x3 = 13, and –x1 + x2 = -8 %3D in…

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Q: B. Is C a real vector space? Explain.

A:

Q: ite a Hilbert proof for the following theorem schema: ((Vx)(A v Bv (¬C))) ^ ((\x)(A → B)) ← ((\x)(C…

A: We want to prove the theorem schema:((∀x)(A∨B∨¬c))∧((∀x)(A→B))⊢((∀x)(C→B)) .

Q: Let f be the send map each Complex numbex 2- Show that (笑)お)ま=(配を)

A: The detailed solution is as follows below :

Q: Find the projection projuv, where u = (1,3,-2) and v = (2,-1,3).

A: Since we kow that the projection of v on u is given by                projuv=u.v||u||2u