linear algebraVECTOR SPACES question 3b basis and column sp

linear algebra..VECTOR SPACES question # 3b basis and column space

Find a basis for the column space of the matrix 15) Find a basis for Col B where 110 -2 0 0 B-0 0 0 0 1 0 1 3 7 2 0 1 -2 7 1 3 and B- 2 4 -9 5 1 and B-0 1 01 3 0 05 -3 -5 16) Let A =11-2-7 16) Let A 1 2 7 -1 3 It can be shown that matrix A is row equivalent to matrix B. Find a basis for Col A. Determine whether the set of vectors is a basis for 17) Given the set of vectors , | (| | | | 0 | | 17 Givon the st f vertr decide which of the following statements is true: A: Set is linearly independent and spans R3. Set is a basis for B Set is linearly independent but does not span Set is not a basis for C: Set spans R3 but is not linearly independent. Set is not a basis for R3 D: Set is not linearly independent and does not span Set is not a basis for R3.

Solution

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17) The vector

Since one is a linear combination of other two they are not linearly independent and cannot form a basis

Last option is right.

B	1	1	0	-2	1	0
	0	0	1	4	1	0
	0	0	0	0	0	1
	0	0	0	0	0	0	C2=C2-C1: C4 =C4+4C1
	0	0	0	0	0	0	C5=C5-C1
	1	0	0	0	0	0
	0	0	1	4	1	0	C4=C4-4C3: C5=C5-C3
	0	0	0	0	0	1
	0	0	0	0	0	0
	0	0	0	0	0	0
	1	0	0	0	0	0
	0	0	1	0	0	0
	0	0	0	0	0	1
	0	0	0	0	0	0
	0	0	0	0	0	0
		Rank	3
	Col	Base	1
			1
			1