Page 123 - Elementary_Linear_Algebra_with_Applications_Anton__9_edition

Find the values of a, b, and c that will make the equation
26.

an identity. and equate the corresponding coefficients of the polynomials on each side

Hint Multiply through by
of the resulting equation.

If P is an matrix such that , then is called the corresponding Householder matrix (named

27. after the American mathematician A. S. Householder).

(a) Verify that if and compute the corresponding Householder matrix.

(b) Prove that if H is any Householder matrix, then and .

(c) Verify that the Householder matrix found in part (a) satisfies the conditions proved in part (b).

Assuming that the stated inverses exist, prove the following equalities.
28.

(a)

(b)
(c)

29. , then
(a) Show that if

(b) Use the result in part (a) to find if

Note This exercise is based on a problem by John M. Johnson, The Mathematics Teacher, Vol. 85, No. 9, 1992.

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