MATH 235 Midterm: MATH 235 UMass Amherst math235_spring11_html exam1-compact
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Exam 1: (16 points) a) show that the reduced row echelon form of the augmented matrix of the system x1 + x2 + 2x4 + x5 = 3 x1 x3 + x4 + x5 = 2. 2x1 + 2x3 2x4 x5 = 3 is . Use at most six elementary row operations. (partial credit will be given if you use more). You are told that the matrix equation a~x = ~b has a unique solution. What can you say about the number of solutions of the system. R2 is the linear transformation given by the formula. Math 235 spring 2011 make-up exam 1 page 2 where ~x ~v is the dot product of ~x and ~v. Use the above formula to nd the matrix a of refl, so that refl(~x) = a~x, for all vectors ~x in r2. R2 the rotation of the plane an angle counterclockwise about the origin.
