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Problem 2. Let c1, C2, C3, C4, C5 be the column vectors of the matrir 3) A = [1 2 1 -3 5 2 35 5 9 1 07 1 (i) Can c; be erpressed as a linear combination of e, and c2? Justify your answer. Write down a linear combination if one erists. (ii) With reference to the reduced row echelon form of A, erplain why the set B = {c1,c2, c4} is a basis for R³. Write down (b]B; the coefficients of the vector b = (5 -3 7)' in the basis B. (iii) Define what it means to say that a set of vectors {v1, V2, ..., Vn} is linearly dependent. Show that the set of column vectors {c1, C2, C3} is linearly dependent. (iv) Explain why {cı,c2} is a basis of the subspace S = Lin{c1, C2, C3, C5} of

Problem 2. Let c1, C2, C3, C4, C5 be the column vectors of the matrir 3) A = [1 2 1 -3 5 2 35 5 9 1 07 1 (i) Can c; be erpressed as a linear combination of e, and c2? Justify your answer. Write down a linear combination if one erists. (ii) With reference to the reduced row echelon form of A, erplain why the set B = {c1,c2, c4} is a basis for R³. Write down (b]B; the coefficients of the vector b = (5 -3 7)' in the basis B. (iii) Define what it means to say that a set of vectors {v1, V2, ..., Vn} is linearly dependent. Show that the set of column vectors {c1, C2, C3} is linearly dependent. (iv) Explain why {cı,c2} is a basis of the subspace S = Lin{c1, C2, C3, C5} of

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.2: Determinants
Problem 17AEXP
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(3) Problem 2. Please provide a typewritten solution! I will be very grateful!

Problem 2. Let c1, C2, C3, C4, C5 be the column vectors of the matrix 3 10 7 1 2 1 -3 5 2 3 5 5 9, 1 A = (i) Can c, be erpressed as a linear combination of c, and c2? Justify your answer. Write down a linear combination if one exists. (ii) With reference to the reduced row echelon form of A, erplain why the set B = {c1, c2, C4} is a basis for R³. Write doun (b]B, the coefficients of the vector b = (5 -3 7)' in the basis B. TOW (iii) Define what it means to say that a set of vectors {v1, V2, ..., Vn} is linearly dependent. Show that the set of column vectors {c1, c2, C3} is linearly dependent. (iv) Explain why {c1,c2} is a basis of the subspace S = Lin{c], c2, C3, C5} of R. Deduce that the subspace S is a plane in R*, and find the Cartesian equation of this plane.
Transcribed Image Text:Problem 2. Let c1, C2, C3, C4, C5 be the column vectors of the matrix 3 10 7 1 2 1 -3 5 2 3 5 5 9, 1 A = (i) Can c, be erpressed as a linear combination of c, and c2? Justify your answer. Write down a linear combination if one exists. (ii) With reference to the reduced row echelon form of A, erplain why the set B = {c1, c2, C4} is a basis for R³. Write doun (b]B, the coefficients of the vector b = (5 -3 7)' in the basis B. TOW (iii) Define what it means to say that a set of vectors {v1, V2, ..., Vn} is linearly dependent. Show that the set of column vectors {c1, c2, C3} is linearly dependent. (iv) Explain why {c1,c2} is a basis of the subspace S = Lin{c], c2, C3, C5} of R. Deduce that the subspace S is a plane in R*, and find the Cartesian equation of this plane.
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