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In Exercises 21 and 22, mark each statement True or False.
Chapter 2, Problem 21E(choose chapter or problem)
In Exercises 21 and 22, mark each statement True or False. Justify each answer.a. A subspace of is any set H such that (i) the zero vector is in H; (ii) u; v; and u + v are in H, and (iii) is a scalar and cu is in H.b. If is the same as the column space of the matrix .c. The set of all solutions of a system of m homogeneous equations in n unknowns is a subspace of .d. The columns of an invertible n × n matrix form a basis for .e. Row operations do not affect linear dependence relations among the columns of a matrix.
Questions & Answers
QUESTION:
In Exercises 21 and 22, mark each statement True or False. Justify each answer.a. A subspace of is any set H such that (i) the zero vector is in H; (ii) u; v; and u + v are in H, and (iii) is a scalar and cu is in H.b. If is the same as the column space of the matrix .c. The set of all solutions of a system of m homogeneous equations in n unknowns is a subspace of .d. The columns of an invertible n × n matrix form a basis for .e. Row operations do not affect linear dependence relations among the columns of a matrix.
ANSWER:Solution:-Step1To findMark each statement True or False. Justify each answer.a. A subspace of is any set H such that (i) the zero vector is in H; (ii) u; v; and u + v are in H, and (iii) is a scalar and cu is in H.b. If is the same as the column space of the matrix .c. The set of all solutions of a system of m homogeneous equations in n unknowns is a subspace of .d. The columns of an invertible n × n matrix form a basis for .e. Row operations do not affect linear dependence relations among the columns of a matrix.Step2a. A subspace of