MATLAB help please!!

Posted on 2015-11-12 12:35:00 in Engineering by LUICE

1. U = round(20 * rand(4)) - 10,
V = round(10 * rand(4))

and set b = ones(4, 1).

(a) We can use the MATLAB function to rank to determine whether the column vectors of a matrix are linearly independent. What should the rank be if the column vectors of U are linearly independent? Compute the rank of U, and verify that its column vectors are linearly indpendent and hence form a basis for R^4. Compute the rank of V, and verify that its column vectors also form a basis for R^(4).

(b) Use MATLAB to compute the transition matrix from the standard basis for R^4 to the ordered basis E = {u1, u2, u3, u4}. [ Note that in MATLAB the notation for the jth column vector uj is U(:, j).] Use this transition matrix to find the coordinate vector c of b with respect to E. Verify that

b = c1u1 + c2u2 + c3u3 + c4u4 = Uc

(c) Use MATLAB to compute the transition matrix from the standard basis to the basis F = {v1, v2, v3, v4}, and use this transition matrix to find the coordinate vector d of b with respect to F. Verify that

b = d1v1 + d2v2 + d3v3 + d4v4 = Vd

(d) Use MATLAB to compute the transition matrix S from E to F and the transition matrix S from E to F and the transition matrix T from F to E. How are S and T related? Verify that Sc = d and Td = c.

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