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6201-16000-MATH-2318 Afeez Amusan & Time Remaining: Quiz: Quiz 2 (1.3, 1.4), Part 1 This Question: 7...
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...
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 o...
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...
Determine if the columns of the matrix form a linearly independent set. Justify your answer. -2...
Determine if the columns of the matrix form a linearly independent set. Justify your answer. -2 -1 01 0 - 1 3 1 1 -6 2 1 - 12 Select the correct choice below and fill in the answer box within your choice. (Type an integer or simplified fraction for each matrix element.) O A. If A is the given matrix, then the augmented matrix represents the equation Ax = 0. The reduced echelon form of this matrix indicates that...
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....
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...
T25-1] 4 1and A0 1-1. Is u in the subset 4 14. Letu-1 0」 of R3...
T25-1] 4 1and A0 1-1. Is u in the subset 4 14. Letu-1 0」 of R3 spanned by the columns of A? Why or why not?
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...
Determine if the columns of the matrix form a linearly independent set. 1 2 - 3...
Determine if the columns of the matrix form a linearly independent set. 1 2 - 3 8 12 37 -6 38 - 1 -8 Select the correct choice below and fill in the answer box to complete your choice. A. The columns are not linearly independent because the reduced row echelon form of [ A o]is | The columns are linearly independent because the reduced row echelon form of [ A 0 ] is B.
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...
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...
Determine if the columns of the matrix form a linearly independent set. 1 2-3 1 2...
Determine if the columns of the matrix form a linearly independent set. 1 2-3 1 2 5 - 4 -2 - 14 2 7 2 Select the correct choice below and fill in the answer box to complete your choice. A. The columns are not linearly independent because the reduced row echelon form of is A 0 B. The columns are linearly independent because the reduced row echelon form ofA 0 is
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...
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...
Determine if the columns of the matrix form a linearly independent set. Justify your answer. -2 -1 01 0 - 1 3 1 1 -6 2 1 - 12 Select the correct choice below and fill in the answer box within your choice. (Type an integer or simplified fraction for each matrix element.) O A. If A is the given matrix, then the augmented matrix represents the equation Ax = 0. The reduced echelon form of this matrix indicates that...
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 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...
T25-1] 4 1and A0 1-1. Is u in the subset 4 14. Letu-1 0」 of R3 spanned by the columns of A? Why or why not?
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...
Determine if the columns of the matrix form a linearly independent set. 1 2 - 3 8 12 37 -6 38 - 1 -8 Select the correct choice below and fill in the answer box to complete your choice. A. The columns are not linearly independent because the reduced row echelon form of [ A o]is | The columns are linearly independent because the reduced row echelon form of [ A 0 ] is B.
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...
Determine if the columns of the matrix form a linearly independent set. 1 2-3 1 2 5 - 4 -2 - 14 2 7 2 Select the correct choice below and fill in the answer box to complete your choice. A. The columns are not linearly independent because the reduced row echelon form of is A 0 B. The columns are linearly independent because the reduced row echelon form ofA 0 is
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