Solved: In Exercises 21 and 22, matrices are n × n and

Chapter 7, Problem 22E

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In Exercises 21 and 22, matrices are n × n and vectors are in Rn. Mark each statement True or False. Justify each answer.a. The expression || x ||2 is a quadratic form.b. If A is symmetric and P is an orthogonal matrix, then the change of variable x = Py transforms xTAx into a quadratic form with no cross-product term.c. If A is a 2 × 2 symmetric matrix, then the set of x such that xTAx = c (for a constant c) corresponds to either a circle, an ellipse, or a hyperbola.d. An indefinite quadratic form is either positive semidefinite or negative semidefinite.e. If A is symmetric and the quadratic form xTAx has only negative values for x ? 0, then the eigenvalues of A are all negative.