Let V₁ = A basis for H is V₂ 1. 4 6, V3 -8 5 - 17 ‚ and H= Span {V₁,V2,V3}. It can be verified that 7v₁ + 2v₂ − 3v3 = 0. Use this information to find a basis for H. 4

Q: 2. How many vectors does any basis of of Max(a+2)(R) contain, if a = max1<i<10 a;?

A: Since, dimension of a vector space is equal to number of elements in basis of vector space.

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Q: , find the change-of-coordinates matrix from the basis B= {1– 2t +t?,3 - 5t + 41,2- 2t + 5t?} to the…

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Q: 4 1 7 - - - - H -3 V2 = 9 14 11 , and also let H = Span{v1, 02, 03}. 7 -2 6 It can be verified that…

A: It can be verified that Using this information we have to find a basis for H.

Q: 2.) Determine whether S = {G.1).(1.0).(2,12,6)} is a basis for R. If it is write u = (6,3,6) as a…

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A: The given vectors are .The aim is to prove the given vectors are basis.

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A: Linearly dependent set

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Q: } 4. You are given that B = {1– 2x + x?, x+ x?, 2 +x – a?} is a basis for P2. (i) Find the…

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Q: Given 1 -3 -1 A = 3 4 -6 8 0 -1 3 1 Find a basis of Ker(A).

A: Given matrix is A=102401-3-134-680-131

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Q: The set B = {3 + 2x², 6 − 2x + 4x², 4x − 13 – 10x²} is a basis for P₂. Find the coordinates of p(x)…

A: The objective of the question is to find the coordinates of the polynomial p(x) = 18x - 54 - 40x^2…

Q: 3) Let S contain vectors of the form f(x) = a + bx + cx² + dx³ : f(-2) = 0 and f'(-4)= 0: Then a…

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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…

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A: Applying nullity definition we have

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A: This belong to linear algebra.we check linear independence for the given vectors and find k so that…

Q: 5 Find w if (w)s = |0| relative to the basis S = {-3 -5 2 } 2 3 w =

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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: 45. Do 000 form a basis for R³?

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Q: 7 Find w if (w)s = |0| relative to the basis S = 3 – 10 3 W =

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Q: 1 3 1 2 A=2 6 4 002 4 I= I Y Z ພ () and 6 = 3

A: Solution to the system

Q: 3 2. (а) Do the vectors vị = -1 -1 form a basis for R³? , V3 = 1 > V2 = -I--- (b) Do the vectors vị…

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Q: Find a basis for the solution space of the given homogeneous linear system. Xy - 3x2 + 3xy - 3x4 = 0…

A: The homogeneous linear system is x1-3x2+3x3-3x4=02x1-5x2+12x3-4x4=0The corresponding matrix form…

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Q: moving targets. If the shooter is an arrowhead whose vertices at any point is in the span of row…

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Q: etermine whether the set S = {1-3xr?, 2x+5x²,1-x+3x²} is basis for P,(R).

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