1. Let l: R2 → R³, l : x+ Ax, where k k %3D 2k –1 9 a.) Establish for which value of k, the linear function l is onto. b.) Establish for which value of k, the linear function l is one to one. c.) Establish for which value of k, it is dim Iml 1 and in this case, find a basis for Kerl.

Q: Suppose S = {r, u, d) is a set of linearly independent vectors. If x = 5r+ 3u+d, determine whether T…

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Q: 8 Let I be the line given by the span of 7 in R³. Find a basis for the orthogonal complement L of L.…

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Q: 4. Apply the principal axis transformation to the curve of second order -x2 + 6xy – y? – 22.x+ 18y –…

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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: 2. Let j = Find the point on the line y x that is closest to j. %3D %3D 26

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Q: { be a basis for R? . Find the vector æ if [æ]R =| 3 Let B 8 x = x = 6. x = x = H 00

A: Given that B=11,21 be the basis for R2. We have to find vector x if xB=23. Since, xB=23 Hence,…

Q: b. Prove that the polynomials p₁(t)=1, p₂(t)=1-t, and p₂ (t)=1+t-t², form a basis for P₂.

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Q: Explain why S is not a basis for R2. S = {(4, 3), (16, 12)} O s is linearly dependent. S does not…

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

A: Given vector is: Pt=1+3t-6t2 Basis set for the vector is given as: B=1-t2, t-t2, 2-t+t2 Then, let…

Q: Let B = {1+t, t – t2, 2t + t2} be a basis for P2. Find [-3+t – t°]B. %3D

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Q: 10. Let F : R² → R² be defined by F(1,0) = (2,4) and F(0, 1) = (5, 8). Find the matrix A…

A: We are given: F:R2→R2 such thatF(1,0)=(2, 4) and F(0,1) = (5, 8) To find matrix representation of…

Q: 2. Let B₁ be the basis 2²e², re², e² of V = span(2²e², zeª, z), and B₂ be the basis of that the map…

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Q: 3. Determine whether the set S = {1 – t, t, 1 + t2} a. Spans P2 b. Is linearly independent с. Is a…

A: Given set is  S = { 1-t ,t , 1+t^2}

Q: Let S = {v1, v2} be a basis of IR? where vi = and What element of R? is determined by the linear V2…

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Q: Define T: R2R? by T(x)= Ax. Find a basis B for R with the property that [T]g is diagonal. 2 -5 A =…

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Q: 32. Let p, (t) = 1 +t², p2(t) = t – 3t², p3(t) = 1 +t – 3t2. || - - a. Use coordinate vectors to…

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Q: 1 3 3. Let S 2 3 2 a. Is span(S)=R³? b. Determine whether S is the basis of R3.

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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: T((a, b)) = (a, a + b, a + 2b). Find range T a

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Q: Determine whether the given set S of vectors is a basis for Pn(R). n=1 : S = {2-5x, 3x, 7+x}

A: To determine whether the given set S of vectors is a basis for Pn(ℝ). n=1,S={2-5x,3x,7+x}

Q: . Consider the set of vectors in R³: It follows that (A) S is a basis for R³ (B) S is linearly…

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Q: Let T : R² → R² by T(x) = A˜, where 1. Find ker T 2. Find a basis for im T. A-[¹₁2] Α = -3 -6

A: 1) Ker T Solution:   1 2     -3 -6   Now, reduce the matrix to reduced row echelon…

Q: Determine whether the set S {1 – t, t, 1 + t²} a. Spans P2 b. Is linearly independent c. Is a basis…

A: As per our guidelines I am solving only 1st for others kindly resubmit the question mentioning that…

Q: Name... 1 0 4 0 5 5 5 2 3 3 3 Let A = Find 1 r - a basis for the solution space of A

A: Transform the matrix to the reduced row echelon form

Q: a) U = { ri + 12 +13 + =0 and r1 + 2r2 + r3 +2r4 = 0

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Q: Which of the following sets of vectors is a basis for R?? {[:]}. 2 3.

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Q: 6. (10 pts.) Let T : V → W be a linear transformation. If dim V = 6, dim W = 5, and T is onto, find…

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Q: 6. Verify that S is an orthogonal basis for R³. Use this to write u as a linear combination of the…

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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: 1 31 3. Let S = }|2 [3. 3 2 a. Is span(S)=R³? b. Determine whether S is the basis of R³.

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