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....
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 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...
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 The following statements are equivalent. 1. ai,a2,..,a, span R" = # of rows of A. 2. A has a pivot position in every row, that is, rank(A) Select one: Oa. No since rank([uv]) < 2 3=# of rows of the matrix [uv b.Yes since rank([uv]) =2 = # of columns of...
(1 point) 5 10 10 Let A = 2 7 10 and b= -5 -8 -11 Denote the columns of A by aj, a2, az , and let W = span {aj, 22,03}. Select Answer 1. Determine if b is in W Select Answer A 2. Determine if b is in {aj, az, az } How many vectors are in {aj, a2, az }? (For infinitely many, enter -1) How many vectors are in W? (For infinitely many, enter -...
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...
(5) Let b = and let A be the matrix . Is b in the range of the linear transformation x↦Ax? Why or why not? We were unable to transcribe this imageWe were unable to transcribe this imageLet b= 1 -3 5 -51 1, and let A be the matrix O 1 -3 5 . Is b in the range of the linear transformation x 2 - 4 4 - 4 Ax? Why or why not? Is b in the...
1-4 - 31 Let A= 3 and b= Show that the equation Ax=b does not have a solution for all possible b, and describe the set 4 26 of all b for which Ax=b does have a solution. How can it be shown that the equation Ax = b does not have a solution for all possible b? Choose the correct answer below. O A. Row reduce the augmented matrix [ a b ] to demonstrate thatſ A b )...
IT a) If one row in an echelon form for an augmented matrix is [o 0 5 o 0 b) A vector bis a linear combination of the columns of a matrix A if and only if the c) The solution set of Ai-b is the set of all vectors of the formu +vh d) The columns of a matrix A are linearly independent if the equation A 0has If A and Bare invertible nxn matrices then A- B-'is the...
a1 a12 a13 a14 bi by b 2 Denote row i in matrix A above as vector a' and row i in matrix B as vector bn' for example, a aan a3 aul Similarly, denote column k in matrix A as vector and column k in matrix B as vector b. a) Does matrix C AB exist? If no, explain why not. If yes, write it out expressing each element ck as the inner product of the relevant vectors defined...