Homework Answers
a)
As there are 2 vectors u and v, of dimension 3, and they ae linearly independent, that's number of pivot points in the matrix [uv] will be 2. Thus, the rank of matrix will be 2. But the number of rows in [uv] = 3. Also, for spanning R3, 3 linearly independent vectors of dimension 3 are required.
Thus, u and v don't span R3.
Thus, A is the correct option.
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2 5 Do the vectors u = and v= 3 7 span R3? -1 1 Explain! Hint: Use Let a, a2,ap be vectors in R", let A = [a1a2..ap...
Let B be the standard basis of the space P2 of polynomials. Use coordinate vectors to...
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1 O -7 5 Let A= 0 2 -2 and b= - 1 Denote the columns...
1 O -7 5 Let A= 0 2 -2 and b= - 1 Denote the columns of A by ay, az, az, and let W= = Span{a,,a,,az}. -34 2 -5 1 a. Is b in {a4, az, az}? How many vectors are in {aq,a2, az}? b. Is b in W? How many vectors are in W? c. Show that az is in W. (Hint: Row operations are unnecessary.] a. Is b in {aq, az, az}? No Yes How many vectors...
Let A = 10-o] 0 2 -3 and b = - 4 4 3 . Denote...
Let A = 10-o] 0 2 -3 and b = - 4 4 3 . Denote the columns of A by a, a, az, and let W = Span{a.a.az). a. Is b in aa.az)? How many vectors are in a .a .a? b. Is bin W? How many vectors are in W? c. Show that a is in W. (Hint: Row operations are unnecessary.] a. Is b in {a .az.az)? No Yes O How many vectors are in aaa? A....
Question 5 1 pts Let V be a subspace of R100, and let S be a...
Question 5 1 pts Let V be a subspace of R100, and let S be a set of vectors such that V = span(S). (S is a spanning set for V.) Build a matrix A using the vectors of S as columns The dimension of V must be equivalent to all of the following EXCEPT: the rank of A the number of "leading 1s" in the RREF of A the number of vectors in S the number of nonzero rows...
1 0 -7 3 Let A= 03 -4 and b= Denote the columns of A by...
1 0 -7 3 Let A= 03 -4 and b= Denote the columns of A by a, a, ay, and let W = Span{a,,a,,a3} -26 2 3 a. Is b in {a,,a,,az)? How many vectors are in {a,az.az)? b. Is b in W? How many vectors are in W? c. Show that az is in W. (Hint: Row operations are unnecessary.] a. Is b in {a,,a,,az)? Ο Νο Yes How many vectors are in {a,,a,a}? O A. Two OB. Infinitely...
6201-16000-MATH-2318 Afeez Amusan & Time Remaining: Quiz: Quiz 2 (1.3, 1.4), Part 1 This Question: 7...
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Please do only e and f and show work null(AT) null(A) T col(A) row(A) Figure 5.6 The four fundamental subspaces (f) Fin...
Please do only e and f and show work
null(AT) null(A) T col(A) row(A) Figure 5.6 The four fundamental subspaces (f) Find bases for the four fundamental subspaces of 1 1 1 6 -1 0 1 -1 2 A= -2 3 1 -2 1 4 1 6 1 3 8. Given a subspace W of R", define the orthogonal complement of W to be W vE R u v 0 for every u E W (a) Let W span(e, e2)...
2-6 3 2- 0 -103-5 Calculate the determinants of A and B -1 4 (use either appropriate row and coum...
please provide detailed and clear solutions for the
following
2-6 3 2- 0 -103-5 Calculate the determinants of A and B -1 4 (use either appropriate row and coumn expansions or elementary row operations and the properties of determinants). Are A and B invertible? Calculate their inverses if they exist 1b. Are the columns of A linearly dependent or linearly independent? Find the dimension of Nul A and the rank of A. What can you say about the number of...
Let B be the standard basis of the space P2 of polynomials. Use coordinate vectors to test whether the following set of polynomials span P2. Justify your conclusion. 1-3t+ 2t?, - 4 + 9t-22, -1 + 412, + 3t - 6t2 Does the set of polynomials span P2? O A. Yes, since the matrix whose columns are the B-coordinate vectors of each polynomial has a pivot position in each row, the set of coordinate vectors spans R3. By isomorphism between...
Question 5: Multiple Choices Assume that vi,2,ig are vectors in R3. Let S span ,02,s and let A be the matrix whose columns are these vectors. Assume that 1 -1 1 0 0 0-3a +b-2c We can thus conclude that A. {6,6,6) is L1. B. The point (1,1 - 1) is in the span of (o,2,s) C. The nullity of A is 2 D. The rank of A is 3 E. B and C are both correct
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Let A = 10-o] 0 2 -3 and b = - 4 4 3 . Denote the columns of A by a, a, az, and let W = Span{a.a.az). a. Is b in aa.az)? How many vectors are in a .a .a? b. Is bin W? How many vectors are in W? c. Show that a is in W. (Hint: Row operations are unnecessary.] a. Is b in {a .az.az)? No Yes O How many vectors are in aaa? A....
Question 5 1 pts Let V be a subspace of R100, and let S be a set of vectors such that V = span(S). (S is a spanning set for V.) Build a matrix A using the vectors of S as columns The dimension of V must be equivalent to all of the following EXCEPT: the rank of A the number of "leading 1s" in the RREF of A the number of vectors in S the number of nonzero rows...
1 0 -7 3 Let A= 03 -4 and b= Denote the columns of A by a, a, ay, and let W = Span{a,,a,,a3} -26 2 3 a. Is b in {a,,a,,az)? How many vectors are in {a,az.az)? b. Is b in W? How many vectors are in W? c. Show that az is in W. (Hint: Row operations are unnecessary.] a. Is b in {a,,a,,az)? Ο Νο Yes How many vectors are in {a,,a,a}? O A. Two OB. Infinitely...
6201-16000-MATH-2318 Afeez Amusan & Time Remaining: Quiz: Quiz 2 (1.3, 1.4), Part 1 This Question: 7 pts 11 of 17 (7 complete) This Vocan each vector in R* be written as a linear combination of the columns of the matrix A? Do the columns of A span R7 24 -7 16 - 1 - 1 1 - 3 0 -6 15 -30 ² 0 3 6 1 1 Can each vector in R4 be written as a linear combination of...
True or False 1. If u, v are vectors in R"and lu + v1l = ||||| + ||v||, then u and v are orthogonal. 2. If p locates a point on a line l in Rand if n # 0 is normal to l, then any other point x on I must satisfy n.x=n.p. 3. A binary vector is a vector with two components which are integers modulo 2. 4. The set of solution vectors to the linear system Ax=b...
Please do only e and f and show work
null(AT) null(A) T col(A) row(A) Figure 5.6 The four fundamental subspaces (f) Find bases for the four fundamental subspaces of 1 1 1 6 -1 0 1 -1 2 A= -2 3 1 -2 1 4 1 6 1 3 8. Given a subspace W of R", define the orthogonal complement of W to be W vE R u v 0 for every u E W (a) Let W span(e, e2)...
please provide detailed and clear solutions for the
following
2-6 3 2- 0 -103-5 Calculate the determinants of A and B -1 4 (use either appropriate row and coumn expansions or elementary row operations and the properties of determinants). Are A and B invertible? Calculate their inverses if they exist 1b. Are the columns of A linearly dependent or linearly independent? Find the dimension of Nul A and the rank of A. What can you say about the number of...
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