Please answer all parts of thequestion.

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Please answer all parts of thequestion. | savvyessaywriters.org

5.(a) (8 points) Suppose that F = R and let V denote a finite-dimensional real inner-product space. If T e L(V) is self-adjoint, then prove, or provide a counterexample for, the statement: T2 + 2T + 21 has only nonzero eigenvalues. (Note: I denotes the identity map on V.) [73 -1 (b) (8 points) Suppose that F = R and that T E L(R2) has matrix with respect to the standard 1 basis {e1, e2} of Rº, where c1, c2 are as in Question 4(a). Justify whether or not T is (i) self-adjoint (ii) normal. (c) (6 points) Suppose F = R. Determine, with justification, the quadratic form corresponding to the matrix 1 0 -27 0 0 4. 1-2 43Please answer all parts of thequestion.

 

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