True or False? In Exercises 8386, determine whether each
Chapter 4, Problem 4.84(choose chapter or problem)
In Exercises 83–86, determine whether each statement is true or false. If a statement is true, give a reason or cite an appropriate statement from the text. If a statement is false, provide an example that shows the statement is not true in all cases or cite an appropriate statement from the text.
(a) The set \(W=\left\{\left(0, x^{2}, x^{3}\right): x^{2}\right.\) and \(x^{3}\) are real numbers} is a subspace of \(R^{3}\).
(b) A set of vectors S in a vector space V is a basis for V when S spans V and S is linearly independent.
(c) If A is an invertible n × n matrix, then the n row vectors of A are linearly dependent.
Text Transcription:
W={0, x^2, x^3): x^2
x^3
R^3
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