Let A = (a, a, as) and B = {b₁,b₂, b3} be bases for V, and let P = {[b₁]A, [b₂]A, [b3]A} (are) satisfied by P for all x in V? AXA = Pxs Both A and B Bxs-PxA Which of the following equat

Q: 2. Let A = 201-18 and /= 2 1 1 2 01 Find A(A+1).

A: A=[2 1      1 2]I=[1 0      0 1]

Q: Let A = {a, az, az} and D = (d, d2, dz} be bases for V, and let P = [d•]a [d2]a [d•]a | Which of the…

A: Given A=a1,a2,a3 & D=d1,d2,d3 be basis for v. and let P=d1A,d2A,d3A.

Q: (2c) Prove or disprove the following statement: “ A UBCANB for any A and B "

A:

Q: Let a=⟨3,−5,5⟩ and b=⟨−1,5,2⟩ Find the component of b onto a

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Q: d) Prove (AV (Vx) BC = (Vx)B(AV C), as long as x not free in A. (Hint: Translate first to Standard…

A: Given,  Prove (AV (Vx)BC = (Vx)b(A V C), as long as x not free in A. (Hint: Translate first…

Q: (Q. +,.) is a subfield of (F = {a + bV5: a, b e Q}, +,.); (F = {a + bv5: a, b e Q}, +,.) is a…

A: A non-empty subset F' of a field F is a subfield of F if F' is closed with respect to the…

Q: Both sets below are bases for P,: P = {pj, P2, P3} = {1+r?, 1+21, t + 21²} Q = {q,, 42» 93} = {1+3t…

A:

Q: Prove that: (5a + 6b|a, b = Z} = Z

A: To prove that .Concepts used:Consider two sets  and . To prove that , we first need to show and…

Q: Let u (9, 9, 8) and = (-9, -1, - 8). = Find proj, (u). -

A:

Q: Are u sure its not 1

A: It is given that a=0 and b=1.

Q: How did they calculate what T does to the elements of B?

A: You want to know "How did they calculate what T does to the elements of B?" We have  B=1, x, x2, x3…

Q: (2) Write v as a lincar combination of u₁, U₂, U3 if possible, where U₁ = (2,3,5), u₂ = (1, 2, 4),…

A: Given that,  V=(10, 1,4)  u1=(2, 3,5), u2=(1, 2,4) , u3=(-2, 2,3)  To find : a, b, c such that…

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: Let V4 = 4 V2 = V3 = -2 Pi -2 P2 2 2 and S = {v1, v2, V3, V4}. Determine whether pl and p2 are in…

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Q: Let u = Compute the following: ū• v = (1, −5, −1) and v = (-5,2,0). v.u ||ū|| ² - 3 (u.v) (-3ū) v =…

A:

Q: Let u=(9,−8)​, v=(1,9)​, and w=(−2,7). Carry out the following computation. Find u+v+w.   |u+v+w|=?

A: Given that  Let u=(9,−8)​, v=(1,9)​, and w=(−2,7) To Find u+v+w.

Q: (b) Let A and Bị be independent; similarly, let A and B2 be independent. Show that in this case, A…

A:

Q: Let a = (5, – 3, 6) and b = (5, 3, 4). (a – 6) × (ã + 6) -| X (a +

A: Given: a→=5,-3,6and b→=5,3,4

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: Is the set {(-3,0,3),(1,-1,2)(4,-2,2), (2,1,3)} of R' linear dependent over R?

A: Clearly dimension of R3 is equal to 3. So at max. we can have 3 independent sets. But here there are…

Q: Show that (AB)T and BTAT are equal.

A: Now,

Q: Let A {a, b} and B = {1, 2}. Give an element of A x B x A.

A: Let M and N be two sets. The Cartesian product, M×N is the set of all possible ordered pairs with…

Q: Let i = (6, – 6, 1) and v = (– 5, 5, – 6). %3D Compute the following: i · i = i. i = - 6(ü - i) = (–…

A: To evaluate the given dot product of vectors u and v.

Q: Let ü = 21 – k and i = i + 3j + k. Compute |ū], |ū], ū × ĩ, and Projzu.

A:

Q: Show that If |z| = 1, then: -1 = Z

A: z is a complex number. z=a+ib |z|=(a+ib)(a-ib)     =a2-b2 if |z|=1, then a2+b2=1

Q: . Let A Find A.

A: Given matrix is Firstly, we find A^2

Q: Let u = (-7,0, — 6) and 7 = (2, 7, 3).

A:

Q: Let u = (-1, 1, 0) and 7 = Compute the following: ú.v= v. ú= = (-7, 6,-5). =

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

Q: compute (BA)T

A: Given information: A=314-201122and B=102 -311 2-41 Calculation: Find BA. BA=102-3112-41314-201122=1·…