MATH 551 Midterm: MATH 551 KSU Sample1Test2 s07

• School: Kansas State University
• Department: Mathematics
• Course: MATH 551
• Professor: All

Document Summary

First sample of test 2 (chapters 3, 4, and 5) Let t : r2 r3 be the linear transformation given by. 4x2 (i) find a 3 2 matrix a such that t x = ax for every x = (x1, x2) r2. (ii) find a basis for range(t ). Is t onto? (iii) let b = [0 0 0] . Find x and y such that the matrix q given by. Find the projection of the vector v = [1, 0, 1, 4] onto the subspace spanned by the vectors u1 = [1, 1, 1, 1] and u2 = [1, 1, 1, 1] . Use cross products to nd the area of the triangle on the plane whose vertices are p = (1, 1), q = (3, 5) and r = (6, 4). Suppose that we have three square matrices a, b, and c such that a is invertible and ab = cat .