7. Prove that p, (t) = 1+t², p2(t) = t – 3t2, p3(t) = 1 +t – 3t, is a basis for P2.

Q: Be S = {v1 = (1,2, 1), v2 = (2,9,0), v3 = (3, 3, 4)} a subset of R and T : R³ → R? T(v1) = (1,0),…

A: Given that  S=v1=1, 2, 1, v2=2, 9, 0, v3=3, 3, 4 be a subset of ℝ3 and     T : ℝ3→ℝ2      Tv1=(1,…

Q: If {e, xe", e2 is a basis of solutions of y" + ay" + by + cy = 0, %3D then a =

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Q: Let Is S a basis for R³?

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Q: 3. Let p₁(x) = ½x(x − 1), p2(x) = −x² + 1 and p3(x) = ½x(x+1). - (a) Show that E = {P1, P2, P3} is a…

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Q: 7. Consider the following basis B3 of P2(R) and the standard basis E of P₂ (R) B3 = {1+x², x +…

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Q: Let W = } t s,t e R -S - 31 5) Show that -6 is in W+. 3 6) Find a basis for W+.

A: given W=s+3tt-s-t  , s t ∈R

Q: 3. The set B = {1-t², t-t²,2-2t + t²} is a basis for P2. Find the coordinate vector of p(t) =…

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Q: -3 Express the general solution of Ax = b where A = 9 9 and -27 3 as x = x, + cx, where x, is the…

A: first we will find the basis for the null space of the matrix a then after finding the solution of…

Q: Determine whether (v₁, v2, v3) is a basis for ³. 1 0, V3 = -4 22 7) v₁ = -2 4, V2 = -8

A:

Q: 3. Let T : R² → R² be defined by T = X Y -x+y x-y

A: 3. Given that  be defined by:

Q: Let s= {(1,3.5). (3. 3, 2). (-1, 1.8)} be a basis for R. If u = (8, 8, 1), then (u), - A) (1 2 1 B)…

A: The solution is given as

Q: Select all that constitute a basis of solutions for the following by the Frobenius method. (x+2)2y"…

A: Find a general solution to the ODE below.This is eligible to use the Frobenius method for linear…

Q: The set B = {1+t², t + t², 1 + 2t + t²} is a basis for P₂. Find the coordinate vector of p(t) = 1 +…

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Q: Prove that y R³ as a linear combination of (5) Is a basis of R³ {0·0·0)}

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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: 2 -3" A = 2 –1 4 4 3 -2

A:

Q: Evaluate the Inverse Laplace transformation of the following functions s²-6 C-1 (-3 $154+35) {3

A: Sol

Q: 4). Find all values of a for which the given vectors form basis for R' -(:) --() ---() a? u = and w…

A: A set B is said to be basis of any vector space if (1) it is linearly independent set. (2)B spans…

Q: Let U = p E 4 (R): 1 -1 p = 0}. Find a basis of U.

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

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Q: a. State the domain and range of the relation shown. Is the relation a function? b. What is the…

A: Note: It is assumed the the function for part b is f(x)=23x-6 .   Let P be a relation, defined as…

Q: Show that B = {1+ 2t, t – t2,t+t2} is a basis for P3. ) Let p(t) = 1+3t +t. Compute [p(t)]s- (a) (b)

A: NOTE: According to guideline answer of first question can be given, for other please ask in a…

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

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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: 5. Consider the basis aj = (1, 2, 3), az = (2, 4, 5), and az = (3, 5, 6) for R] × 3. Consider t E…

A: Given α1 =1, 2, 3, α2 =2, 4, 5, α3 =3, 5, 6 is the basis of R1×3 So let α = α1, α2, α3 Let τ = α…

Q: -3 Express the general solution of Ax = b where A = and -9 27 b = as x = x, + cxn where x, is the…

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Q: {1+2t – t3,3 +t+4t2, 6t2 + 263, 4 – 5t2} (b) B = {1 – 212, 2t + 31, 2 + 3t – 3t2, -1 – t+t? + 31³}…

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Q: 14. The set B = {1 – 1², t – t²,2 – 2t + t²} is a basis for P2. Find the coordinate vector of p(t) =…

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Q: 3. Suppose that {v1, v2, V3} is a basis for V and p:(v;) = dij. Let %3D W1 = 2v1 + v2, W2 = v1 -…

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Q: If {x, a} is a basis of solutions of a?y" + axy' + by = 0, then a = (A) -2 (в) 2 (C) -3 (D) 3 (E)…

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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: Let TilPe P. Tlax²+ bx+c) = 20x+ b. Then the basis of NIT) is O True O False

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Q: 2. For the differential equations below, write in standard form, and name the type of equation. Then…

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Q: 5. Let v1, V2, ..., Vn € R". Let A be then x n matrix whose j-th column is v; (j = 1, 2, n), that…

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Q: 2 1-1] Let T : R³ → R³ be defined by T'(x) = Ax where A = -1 3-2 0 3 4 a) Find a basis for the…

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