-5 X. Hint: The image of a spanning set is a -15 Let V = R2x2 be the vector space of 2 x 2 matrices and let L :V →V be defined by L(X) = -3 spanning set for the image. a. Find L = b. Find a basis for ker(L): { } c. Find a basis for ran(L): { }

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A: Given: L:R3→R3 and is defined by, L100=110L010=201L001=101 It can be further defined as,…

Q: 10 Let V = R2x2 be the vector space of 2 x 2 matrices and let L :V → V be defined by L(X) = -2 5 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

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A: 1) Given that D=d1,d2,d3F=f1,f2,f3f1=2d1-d2+d3f2=3d2+d3f3=-d1+2d3 To find (a) and (b):

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A: Since you have asked multiple question, we will solve the first question for you. If you want any…

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A: We have to find the transition matrix for the given basis.

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Q: (d) Let V = R³, W = R² and define T : V → W by T: (x1, x2, x3)(x₁ - x2, X2 - x3). Find the kernel of…

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Q: -2 Let T : R? → R² be defined by Tx = Ax where A = Find a basis 10. B for R² such that the B-matrix…

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Q: 4. Let B = and observe that B is a basis for R³. Using the vectors in 3, find an orthogonal basis…

A: The solution are next step..

Q: 1. In the natural basis of vector space R³, the linear transformation p has matrix A, where (4 -8 8…

A: Given a matrix                           A=4-881-241-34 For this we compute the characteristic…

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Q: 4.) Let P3 be the vector space of polynomials of at most degree 3. (a) Show that the set {1, x, x²,…

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Q: Please give correct answer

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Q: 3(a) Prove that if the list X1, X2 is a basis for a vector space V, then the list ax1, bx1 + cx2 is…

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Q: = 13² 1² for Consider the ordered bases B=( a and C= a. Find the transition matrix from C to B. TB =…

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Q: 8. Let W = Span{v1, v2}. Find an orthonormal basis for W. Vị = -2 , V1 = 4 2

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Q: 2 -6 Consider the matrox transformation T:R+ R defined by T(X)= AX. where A= -1 Which of the…

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Q: Use the above to answer the following questions. 7.1 Find a basis for the nullspace of A. 7.2 Find a…

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