Solution Found!
Answer: In Exercises 21 and 22, mark each statement True
Chapter 4, Problem 21E(choose chapter or problem)
In Exercises 21 and 22, mark each statement True or False. Justify each answer.a. A single vector by itself is linearly dependent.b. c. The columns of an invertible n × n matrix form a basis for .d. A basis is a spanning set that is as large as possible.e. In some cases, the linear dependence relations among the columns of a matrix can be affected by certain elementary row operations on the matrix.
Questions & Answers
QUESTION:
In Exercises 21 and 22, mark each statement True or False. Justify each answer.a. A single vector by itself is linearly dependent.b. c. The columns of an invertible n × n matrix form a basis for .d. A basis is a spanning set that is as large as possible.e. In some cases, the linear dependence relations among the columns of a matrix can be affected by certain elementary row operations on the matrix.
ANSWER:Solution 21EStep 1 of 5(a)Consider the statement,“A single vector by itself is linearly dependent.”Let be any vectorWrite the vector as a linear combination. , is scalarAs , so the scalar must be equal to zero, Thus the single nonzero vector is linearly independent.If then only the vector is linearly dependent.Hence the statement is .