in M₂ (R). (1) Find a basis of the span of (3)-(1)-(7)

Q: 59. In R4, given 2 nullspaces 1 2 00 1 V : |-1 0 -1 m 0- Find m such that dim(U n V) is max. Find…

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Q: (1' '3' Consider vị = | 2 V2 = 9 and v3 = 3 ) as vectors in R3. 4 Let T: R3→R2 be a linear…

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Q: Let B = {B]. A} mation x→→ Ax. =[%] be a basis for R2 and A = Find the B-matrix for the transfor-

A: Given that The transformation is

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

A: 3. Given that  be defined by:

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: 10. (a) Define: Basis 6 -1 -2 2 3 -4 5 8 (c) Find dim(nul(B)) and dim(col(B)), does your result…

A: The given matrix B=-36-11-11-223-12-458-4. We have find a basis for the null space of B and the…

Q: 0 1 0 S = {(1 3)·(¦¯¯^¹)· (² ¦ ). ( -º2³)} 03 4 0 23 2 is independent or not and if it is not,…

A: Recall the definition of linear independence i.e non-zero span of vectors must be non-zero. If a…

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: 1. Consider the linear map T : R[X]deg<3 → Mat2,2(IR) given by f(0) f'(1) T(f) = (-1) F(2) Let B =…

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Q: please explain part d because i am confused by the second and third part of part d.

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Q: (4) 10. Let H = {r+2x2, 1+ ka?, k + (2k + 3)r2} (a) For what value(s) of k is H linearly dependent?…

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

Q: 9. Find an orthonormal basis for P[r]3 with a basis 1, 2, 2² if the inner product on P[r]3 is…

A: We have to find the orthonormal basis for  with a basis The inner product is defined by

Q: 5 Find w if (w)s = |0| relative to the basis S = {-3 -5 2 } 2 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: Find a basis of solutions by the frobenius method. Xy'' + 2y' + xy = 0

A: To find a basis of solutions for the differential equation xy″+2y′+xy=0 using the Frobenius method,…

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: How can I find [L] from basis B to basis C, if basis B = {1 + x + x^2, 1 + x, 2x + x^2} and basis C…

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Q: 7) The coordinates vector of w.3) in R² relative to the standard basis in R² is A) (:) 이(글) 8) The…

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Q: 9. Find a basis for the hyperplane a where a-(2, 1, -3).

A: Any two linearly independent vectors which are orthogonal to the given a are forms a orthogonal…

Q: Let k1, k2, ..., ks be positive integers and consider sx s block diagonal matrix J(A) given by Jk₁…

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Q: 8. Let S be the standard basis for R2, and let B = {v₁, v₂} be the basis in which v₁ = (2, 1) and v₂…

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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: Consider the following two bases of R: {(E) () 0} {{:) () B = C = 4 What is the change-of-basis…

A: The base change from B to C is given by   =  B-1C

Q: If {1, e²x, xe²*} is a basis of solutions of y"" + ay" +by' + cy = 0, b= 2 (b) -2 -4 (d) 4 (e) 0

A: We can start by substituting the basis functions into the differential equation and solving for a,…

Q: Let wi = w2 = and set B = (w1,w2). Then B is a basis of R². (C 9). If T : R? → R² has matrix with…

A: We have to find first general formula for T the the sum of the coefficient

Q: Let 1 0 1 2 0 -1 -1 1 0 0 1 1 0 1 1 and let T: R6 →→ R5 be defined by T(x) = At. (a) Find a basis…

A: Given matrix is  and (a) Obviously  basis for  is same as basis for column space of A .         Now…

Q: 9. Consider the orthonormal basis S for R³ S = (v₁,v₂,v,} where v₁ = (0,1,0) and v₁ = Let u = V₂ = =…

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Q: 1 2 -1 1 (VI). (12' ) Let A=| 0 2 -1 0 Find a basis for the row space of A and a 1 4 -2 1 basis for…

A: Answer and explanation is given below..

Q: On P(R), consider the inner product given by 1 (p · q) = ["'p(x)q(x) dx. Apply the Gram-Schmidt…

A: Given inner product is Let Using Gram Schmidt Process to make  orthogonal. Let Using Gram Schmidt…

Q: = {(-+). (1)·()} Let T: R³-R², C canonical basis of R² and B = (₂² +z), then [7] corresponds to…

A: Let V and U be finite dimensional vector spaces of dimensions n and m respectively. Let…