4.2. Find matrix P that makes matrix A diagonal, that is, D= lAP where D is a diagonal matrix.

4.3 Find the n-th power of matrix A, that is, A". It is not necessary to explicitly compute . You can just express the result in terms of P and .

5. Let matrix that is composed of tirere column vestors Find the QR-decompostion of A, ie, A=OR where Q is a 3xs matix with ortionormal colann vectors and R is a 3x3 invertible upper triangular matrix. Hint: use Gram-Schmidt process to transform the basis vectors of the three column vectors in A into an orthogonal basis, and then normalize the orthogonal basis vectors to obtain an orthonormal basis corresponding to the column vectors q1,q2,q3 in matrix Q. The entry of matrix R is the inner product of vectors .

6. Let function f(x) be defined for -L sx sL. The Fourier series of f(x) isFind the coefficients of the Fourier series for the function f(x)= x -π ≤ x ≤ π .

1.A computer has six tape drives, with n processes competing for them. Each process may need two drives. For which values of n is the system deadlock free?

(a)

(b)

(a) What is a lower bound on the number of page faults?

(b) What is an upper bound on the number of page faults?

(a) What would be the size of the smallest file allowed in bytes?

(b) What would be the size of the largest file allowed in bytes?

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