PDF Reader X 230prac1f20.pdf X + . .. Enter Search Text ? BOTA 1 / 1 55% Q E X Math 2300 Practice Problems 1. Deternine the solutions to the linear system cty+z=1 -2x - 42 = 4 y - z = 3 How is your answer related to the solutions of the corresponding homogeneous system? 2. If a matrix A has a reduced row echelon form describe the solution set of Ax = 0. If the first two columns of A are and -NO , find the matrix A. 3. What property must b have in order for Ax = b to have a solution (that is, for the system to be consistent)? Explain your answer. 4. If a homogeneous system Ax = 0 has a nontrivial solution, what does that say about the columns of A? 5. Construct a (2 x 3)-matrix A such that the solution set of Ax = 0 is a line in R3. 6. Suppose {v1, V2} is a linearly independent set in ". Show that {v1, v1 + v2} is also linearly independent. 7. Define T : R2 - R3 by T(x, y) = (x, 0, y). Find a matrix A where T(x) = Ax. Is T a linear transformation? 8. Show that if 7 : R" -> R" is a linear transformation, then T(0) = 0. Type here to search O PDF 1:14 PM 9/19/2020