a) Find the coordinate vector of x = of R³. To with respect to the ordered basis *- {0-1-8} E [x] E E = 2 -14 -88

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.

Q: Let 6 2 A =| 9 5 11 8 L = 3 1 and 1 4 U = | 0 2 -1 Find scalars r, s, t, and p so that LU = A.

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Q: Explain why S is not a basis for R2.S = {(−3, 2)}

A: We know the definition of basis, let V be a vector space. Let B be a set of vectors in vector space…

Q: 5.) Let B = {(1,1, –1), (1,–1,1), (-1,1,1)}, and B' = {(1,0,0), (0,1,0), (0,0,1)} be bases for R³,…

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Q: Consider the bases for M2x2(R) given by a' : and a the stan- dard basis. For the transformation T :…

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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: Find a basis for the span of {[1, 3]", [-1, 3]T, [1, 4]T , [2, 1]T}

A: We have to find a basis for the span of   [1, 3]T, [-1, 3]T, [1, 4]T, [2, 1]T .

Q: Determine whether the set of polynomials 10. i (I+ x2, x + X2, 2 t x} is a basis forr Pe (TR).

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Q: Verify that the polynomials 2 – x², x' – x, 2 – 3x² and 3 – x' form a basis for P3(x). Express cach…

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Q: Apply the Gram-Schmidt process to find an orthogonal basis for S. 2 pan{ [ ² ]- [8]} 6 S = span (8)

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Q: (1x30'+ 3xD+1)y:о, усідів, у'(1)-о утобу'+0.09у= y (0) = 2.2, y' (0) = 0.14 -0.3x -o-3x e хе

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Q: TRANSCRIBE THE FOLLOWING TEXT IN DIGITAL FORMAT

A: Given that

Q: Under what condition on the numbers m1, m2, ... , m9 do these three parabolas give a basis for the…

A: To Find: The condition on m1,m2,...,m9 for which m1+m2x+m3x2,m4+m5x+m6x2,m7+m8x+m9x2 forms a basis…

Q: Let p₁ (t) = 7+t², P₂ (t)=t-2t², P3(t) = 2+t-4t². Complete parts (a) and (b) below. a. Use…

A: The polynomials p1t, p2t and p3t belongs to the vector space P2 because P2 contains all the…

Q: | Lat T: R R, and S: R + R", *+: a) Find (So 7] and (T o S). (b) Find a basis for the keruel of So7…

A: We have to answer the following for the given maps.

Q: Select all that constitute a basis of solutions for the following by the Frobenius method x²y" + 6xy…

A: Given differential equation isx2y″+6xy′+(4x2+6)y=0Rewrite the equation asy″+6xy′+4x2+6x2y=0Here…

Q: {} Find in R² whose coordinate vector relative to the basis B is [x]B Let B = x = 12 -5 -6 [:] 5

A: Introduction: The coordinate vector of an element of vector space related to basis is the vector…

Q: 4. Determine whether the given vectors form a fundamental set on the interval (-0, 00). -()-. X1 =…

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Q: –10 S = l2] ] 13 2. 2.

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Q: Write the following equations using index notation and Einstein summation convention: (a) (a b)(b c)…

A: The following are the rules in the Einstein's summation convention having the index notation:1) The…

Q: V = [X1 5 1;3 X2 2;4 0 6] A. V(:,2) B. diag(V) C. V(1,1) + V(2,1) + V(2,2) + V(3,2) D. 10: X1 : 40…

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Q: Find the coordinate vector of p(x) in P., relative to the basis S= {p,.P.-P;}, where p(x) =…

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Q: now that B = {x, r³ + 2x² + 4, x² + 2, 1} is a basis for P3.

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Q: (8) (a) Find a basis B3 of the plane 2x1 - 3x2 + 4x3 (2,3)T. - 0 such that (1, 2, 1)

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Q: -2 11 5 100-10 The reduced row echelon form of the matrix A = Find a basis for the null space of A…

A: Note that null(A)=null(M), where M is in the echelon form of A  and the dimension of null(A) is…

Q: 0 -88-8 and 0 Find an orthogonal basis for the space spanned by 4 2 6 4

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Q: Find the modulus = (ii) -1+3i 2-7 O Locate the numbers Z,+7 and Z,=Zz Vectorially when : + bi) ž,-…

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Q: 5. Determine whether the following three vectors v, = (1, 2, 3, 4), = (0, 1, 0, -1) and v, = (1, 3,…

A: To determine the given vectors form of basis for or not.

Q: 4. Consider f(x) = sinr. If f(x) is interpolated by p2(2) polynomial with the nodes {-7.0, }, the…

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Q: 5. Consider V=R². Find the coordinates of = (10, 20) with respect to the ordered basis ß= [(1, 1),…

A: we will find the coordinate vector with respect to the given basis.

Q: 6. Let B be the following ordered basis for R?: в %3 {(1,—1), (2, -3)} . Find the coordinate vector…

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Q: [ -7 4 -4 4 -1 3 -7-4-1-6] A nonzero vector with integer entries in the null space of T'is Let T =…

A: Given: T=-74-4413-7-4-1-6 To Find: Non-zero vector of null space of T.