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# hwB07 - B S 7.2 P 2.4 in textbook Let G be a m × 2 matrix...

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ENEE 241 02* HOMEWORK ASSIGNMENT 7 Due Fri 02/15 (i) (2 + 2 pts.) Suppose a 3 × 3 matrix A satisﬁes A 1 0 0 = - 4 2 1 , A 0 1 0 = 3 - 2 2 and A 0 0 1 = 0 - 1 2 . Find A and compute A 1 0 1 (ii) (10 pts.) If B = 0 1 0 0 0 1 1 0 0 and x = [1 2 3] T , determine the following: (a) Bx , and explain the resulting transformation of x in words. (b) B 2 x = B ( Bx ) (c) B 3 x = B ( B 2 x ) (d) B 3 x - x (e) What would the result of part (d) be if x = [ x 1 x 2 x 3 ] T for arbitrary real numbers x 1 , x 2 , and x 3 ? (iii) (6 pts.) Study the function FFTSHIFT in MATLAB. Ignore the references to spectra and frequencies, and focus on how FFTSHIFT transforms a vector of odd or even length. Based on your observations, ﬁnd the matrix C which is equivalent to FFTSHIFT , i.e., C*x equals fftshift(x) . Do so in the cases where length(x) equals 7 and 8. Solved Examples S 7.1 ( P 2.3 in textbook). If B 1 0 = 3 - 2 - 1 and B - 1 1 = 4 7 2 , determine B 2 - 1 What are the dimensions of the matrix

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Unformatted text preview: B ? S 7.2 . ( P 2.4 in textbook). Let G be a m × 2 matrix such that G •-1 1 ‚ = u and G • 2 1 ‚ = v Express G • 3 3 ‚ in terms of u and v . S 7.3 . ( P 2.1 in textbook). In MATLAB, enter the matrix A = [1 2 3 4; 5 6 7 8; 9 10 11 12] (i) Find two-element arrays I and J such that A(I,J) is a 2 × 2 matrix consisting of the corner elements of A . (ii) Suppose that B=A initially. Find two-element arrays K and L such that B(:,K) = B(:,L) swaps the ﬁrst and fourth columns of B . (iii) Explain the result of C = A(:) (iv) Study the function RESHAPE . Use it together with the transpose operator .’ in a single (one-line) command to generate the matrix • 1 2 3 4 5 6 7 8 9 10 11 12 ‚ from A ....
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hwB07 - B S 7.2 P 2.4 in textbook Let G be a m × 2 matrix...

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