1 Calculate the following things: 24 204 2 (a) A basis for the rowspace, column space,...

 

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1 Calculate the following things: 24 204 2 (a) A basis for the rowspace, column space, and nullspace of 3 61029 483067 . (b) A basis for the vector space of 2 x 3 matrices A such that [3]-[88 8] 00 (c) An extension of the linearly independent set {(1,1,0,0), (1,1,2,2)} to a basis of Rª. (d) A subset of the vectors ((1,2,1), (2, 1,5), (1. -1,4), (0,-1, 1)) that give a basis of their span. (e) Bases for the kernel and image of the linear transformation S: M₂x2 (R)→ M₂x2 (R) with S(A)=A+A¹. (f) The matrix (S associated to the linear transformation S: M2x2(C)→ M₂x2(C) with S(A) = A +AT, where 3 = -{[8][8][8][8]} 000 000 (g) The matrix [7] associated to the linear transformation T: P₁(R)→ P(R) with P(p) = rp'(x) - p(x). where 8 (1-1, 1-², 1-³,²+r) and = {1,2,²,³}. (h) The "angle" between the functions f(r) = 1 +sinr and g(x) - 1-sinz in C[0, 2] with inner product (f.9) f(x)g(x) dr. (i) The coordinate vector (vl, where v= (9.7.-8) and 3(e.e.es) is the orthogonal basis {(-1,1,2), (2,0,1), (1,5,-2)) of R. (j) An orthogonal basis for P. (R) under the inner product (p.q)- f p(r)q(r) dr. 1 Calculate the following things: 24 204 2 (a) A basis for the rowspace, column space, and nullspace of 3 61029 483067 . (b) A basis for the vector space of 2 x 3 matrices A such that [3]-[88 8] 00 (c) An extension of the linearly independent set {(1,1,0,0), (1,1,2,2)} to a basis of Rª. (d) A subset of the vectors ((1,2,1), (2, 1,5), (1. -1,4), (0,-1, 1)) that give a basis of their span. (e) Bases for the kernel and image of the linear transformation S: M₂x2 (R)→ M₂x2 (R) with S(A)=A+A¹. (f) The matrix (S associated to the linear transformation S: M2x2(C)→ M₂x2(C) with S(A) = A +AT, where 3 = -{[8][8][8][8]} 000 000 (g) The matrix [7] associated to the linear transformation T: P₁(R)→ P(R) with P(p) = rp'(x) - p(x). where 8 (1-1, 1-², 1-³,²+r) and = {1,2,²,³}. (h) The "angle" between the functions f(r) = 1 +sinr and g(x) - 1-sinz in C[0, 2] with inner product (f.9) f(x)g(x) dr. (i) The coordinate vector (vl, where v= (9.7.-8) and 3(e.e.es) is the orthogonal basis {(-1,1,2), (2,0,1), (1,5,-2)) of R. (j) An orthogonal basis for P. (R) under the inner product (p.q)- f p(r)q(r) dr.

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The image shows multiple parts a to j of a question where the task is to calculate various mathematical items such as a basis for the row space column space and null space of a matrix as well as other ... View the full answer