Question
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Let A = and B = . It can be shown that matrix A is row equivalent to matrix B. Find a basis for Col A. {[-1 1 2 3 ]}, [3 -2 -4 -6], [7 -7 -9 -11], [2 -1 -5 -9], [0 3 1 -1]} {[-1 1 2 3], [3 -2 -4 -6], [2 -1 -5 -9]} {[1 0 0 0], [-3 1 0 0], [-7 0 5 0]} {[-1 1 2 3], [3 -2 -4 -6], [7 -7 -9 11]} If the set W is a vector space, find a set S of vectors that spans it. Otherwise, state that W is not a vector space. W is the set of all vectors of the form [a - 6b 2 6a + b -a - b], where a and b are arbitrary real numbers. S = {[1 0 6 -1], [-6 0 1 -1], [0 2 0 0]} S = {[1 2 6 -1], [-6 0 1 -1] S = {[1 0 6 -1], [-6 2 1 -1] W is not a vector space. Given the set of vectors S = {[1 0 0], [0 1 0], [0 0 1], [0 1 1]}, which of the following statements are true? S is linearly independent and spans R3. S is a basis for R3. S is linearly independent but does not span R3. S is not a basis for R3. S spans R3 but is not linearly independent. S is not a basis for R3. S is not linearly independent and does not span R3. S is not a basis for R3. D A C B Find a matrix A such that W = Col A. W = {[2r - t 5r - s + 2t s + 5t r - 3s + t]: r, s, t in R} A = A = A = A = Find the vector x determined by the given coordinate vector [x]B and the given basis B. B = {[-3 2], [0 1]}, [X]B = [6 5] x = [-18 5] x = [-15 -7] x = [-18 -7] x = [-3 -1]
Explanation / Answer
1)b
2)d
3)d
4)a
5)c
