
Determine whether S is a basis for R. S = {(2, 4, 3), (0,4,3), (0, 0,3)} OS is a basis for R3 S is not a basis for R3. If S is a basis for R3, then write u = (6, 8, 15) as a linear combination of the vectors in S. (Use S1, S2, and sz, respectively, as the vectors in S. If not possible, enter IMPOSSIBLE.) us
Determine whether S is a basis for the indicated vector space. S = {(0,4, -1), (5, 0, 3), (–10, 20, -11)} for R3 O S is a basis of R3. O S is not a basis of R3.
Consider T:R4 → R3 with 1 [T) 3 2 -4-1 0 0 5 7 8 10 4 3 -20 -6 1 0 0 5 om Find a basis for image(T). What is dim(image(T))? Convert image(T) to relation form.
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B Lets-(0+4 r+e34 r3 ) is aha is ofs. +aite 2+3a3 =0]. Verify that iS a basis of S In exercises 8 12 decide if the sequence B is a basis for the space S of exercise 7 See Method (5.3.2). Note that if there are the right number of vectors you still have to show that the vectors belong to the subspace S
B Lets-(0+4 r+e34 r3 ) is aha is ofs. +aite 2+3a3 =0]. Verify that iS...
Let S = {(-6, 0, 3),(0, -7, -7),(0,2,0)} be an ordered basis of R3. Let v be a vector in R3, v=(4,7,-1) You calculate V in the basis of S. And get: (a1, a1, a3) What is the value of a3?
0 0 Determine whether the set O 0 is a basis for R3. If the set is not a basis, determine whether the set is linearly independent and whether the set spans R3. 0 Which of the following describe the set? Select all that apply. A. The set is a basis for R3. B. The set is linearly independent. C. The set spans R3. D. None of the above are true.
QUESTION 3 Let S = {(6, 0, 3),(0,5,5),(0,1,0)} be an ordered basis of R3. Let v be a vector in R3, v=(4,7,-1) You calculate V in the basis of S. And get: (a1, a1, a3) What is the value of a3?
Find a basis for the subspace of R3 spanned by S. S = {(4, 4, 9), (1, 1, 3), (1, 1, 1)} STEP 1: Find the reduced row-echelon form of the matrix whose rows are the vectors in S. 1 0 0 1 0 0 0 x STEP 2: Determine a basis that spans S. 35E
5. Given a linear map f R3R3 if V Vi, V2, va) is a basis of R3, and further, a) State the defining matrix of f under the basis vi, V2, vs) -3 2 0 b) Let W-(w1, w2, w3) be another basis of R3 and P42 be the change- 01-1 of-coordinate matrix from V to W. Let A be the defining matrix for f under the basis W diagonalize A.
5. Given a linear map f R3R3 if V...
1. Consider the following two bases for R3. --{():(1) 0)) -= {(8) 0) (1) and (a) Compute Ps-B where S is the standard basis for R. (b) Compute PB-B!. (c) Compute PB:~B. (d) Fill in the blanks. Do your computations on scrap paper. -) (1) (-3, 1, 2), = ( —, - (ii) (1, -1, 0 )B= ( -_- (iii) (0, 3, -1 ),= (-