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.

A:

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,…

A:

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

A:

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

A:

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).

A:

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

A:

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

A:

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

A:

Q: (1) Let B = {√₁, 72, 73} be the basis of R³ defined by 1 *-(). *- (). *-(1) ), = = = Find the dual…

A:

Q: –10 S = l2] ] 13 2. 2.

A:

Q: Show that (2 – 2x², 3x – 1, −1) is a basis for P. 3z

A: A set of polynomials is called the basis of  if it has at least 3 linearly independent at most 3…

Q: Is v = |1a vector in the span of S = }|2| Use Gaussian elimination to support your answer.

A: To check v=111 a vector in a span of S=123, 012, -201 or not.

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…

A:

Q: The percentage of female high school graduates who enrolled in college is given in the table below.…

A: Let x represent time(in years) since 1970, and let y represent the corresponding percentage of…

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

A:

Q: hich of the following sets of polynomials form a basis for P2? 1, p2 1- 5х, рз || (i) p1 х, р4 (i)…

A:

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

A:

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: Find a particular solution of the equation y4 -y3 - y" - y' - 2y = 8x^5:

A:

Q: Expand x = (a, b, c, d) with respect to the orthogonal basis of: 2 -1 1 Vị = V2 -2 3 Express your…

A: Note: Observe that the given orthogonal basis spans only two dimension subspace of ℝ4, therefore the…

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

A:

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

A:

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

A:

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: The functions 1, cos x, sin x, cos 2x, sin 2x, ... are a basis for Hilbert space. Write the…

A:

Q: If {e", xe", e2a is a basis of solutions of y" + ay" + by' + cy = 0, then a = (A) -2 (В) 2 (С) —4.…

A:

Q: Let F = sin (7x + 5z)i – 6ye*z k. Calculate div(F) and curl(F). (Express numbers in exact form. Use…

A:

Q: The set B basis: [x]B = = - 3 -3 Find the coordinates of the vector x = -6 5 is a basis for R². [15]…

A: