29 17.19.501·[8]·L-812-3[3]5418.20.-245CO300In Exercises 21 and 22, mark each statement True or False. Justifyeach answer on the basis of a careful reading of the text.21. a. The columns of a matrix A are linearly independent if theequation Ax = 0 has the trivial solution.b.If S is a linearly dependent set, then each vector is a linearcombination of the other vectors in S.c. The columns of any 4 x 5 matrix are linearly dependent.d.If x and y are linearly independent, and if {x, y, z) islinearly dependent, then z is in Span {x, y).22. /a. Two vectors are linearly dependent if and only if they lie22.on a line through the origin.b. If a set contains fewer vectors than there are entries in thevectors, then the set is linearly independent.c. If x and y are linearly independent, and if z is inSpan {x, y), then {x, y, z) is linearly dependent.d. If a set in R" is linearly dependent, then the set containsmore vectors than there are entries in each vector.In Exercises 23-26, describe the possible echelon forms of thematrix. Use the notation of Example 1 in Section 1.2.23. A is a 3 x 3 matrix with linearly independent columns.32E0eei 17.19.501·[8]·L-812-3[3]5418.20.-245CO300In Exercises 21 and 22, mark each statement True or False. Justifyeach answer on the basis of a careful reading of the text.21. a. The columns of a matrix A are linearly independent if theequation Ax = 0 has the trivial solution.b.If S is a linearly dependent set, then each vector is a linearcombination of the other vectors in S.c. The columns of any 4 x 5 matrix are linearly dependent.d.If x and y are linearly independent, and if {x, y, z) islinearly dependent, then z is in Span {x, y).22. /a. Two vectors are linearly dependent if and only if they lie22.on a line through the origin.b. If a set contains fewer vectors than there are entries in thevectors, then the set is linearly independent.c. If x and y are linearly independent, and if z is inSpan {x, y), then {x, y, z) is linearly dependent.d. If a set in R" is linearly dependent, then the set containsmore vectors than there are entries in each vector.In Exercises 23-26, describe the possible echelon forms of thematrix. Use the notation of Example 1 in Section 1.2.23. A is a 3 x 3 matrix with linearly independent columns.32E0eei

Question

29 17.19.501·[8]·L-812-3[3]5418.20.-245CO300In Exercises 21 and 22, mark each statement True or False. Justifyeach answer on the basis of a careful reading of the text.21. a. The columns of a matrix A are linearly independent if theequation Ax = 0 has the trivial solution.b.If S is a linearly dependent set, then each vector is a linearcombination of the other vectors in S.c. The columns of any 4 x 5 matrix are linearly dependent.d.If x and y are linearly independent, and if {x, y, z) islinearly dependent, then z is in Span {x, y).22. /a. Two vectors are linearly dependent if and only if they lie22.on a line through the origin.b. If a set contains fewer vectors than there are entries in thevectors, then the set is linearly independent.c. If x and y are linearly independent, and if z is inSpan {x, y), then {x, y, z) is linearly dependent.d. If a set in R&#34; is linearly dependent, then the set containsmore vectors than there are entries in each vector.In Exercises 23-26, describe the possible echelon forms of thematrix. Use the notation of Example 1 in Section 1.2.23. A is a 3 x 3 matrix with linearly independent columns.32E0eei 17.19.501·[8]·L-812-3[3]5418.20.-245CO300In Exercises 21 and 22, mark each statement True or False. Justifyeach answer on the basis of a careful reading of the text.21. a. The columns of a matrix A are linearly independent if theequation Ax = 0 has the trivial solution.b.If S is a linearly dependent set, then each vector is a linearcombination of the other vectors in S.c. The columns of any 4 x 5 matrix are linearly dependent.d.If x and y are linearly independent, and if {x, y, z) islinearly dependent, then z is in Span {x, y).22. /a. Two vectors are linearly dependent if and only if they lie22.on a line through the origin.b. If a set contains fewer vectors than there are entries in thevectors, then the set is linearly independent.c. If x and y are linearly independent, and if z is inSpan {x, y), then {x, y, z) is linearly dependent.d. If a set in R&#34; is linearly dependent, then the set containsmore vectors than there are entries in each vector.In Exercises 23-26, describe the possible echelon forms of thematrix. Use the notation of Example 1 in Section 1.2.23. A is a 3 x 3 matrix with linearly independent columns.32E0eei

Accepted Answer

As you have mentioned that  I have to answer only Q-29

29. Construct 3 x 2 matrices A and B such that Ax = 0 has only the trivial solution and Bx = 0 has a nontrivial solution.