linear algebra

1. Consider the following system of equations. f x1 – 5×2 = 1 3×1 – 7×2 = 5 Write the augmented matrix for the system. Reduce the augmented matrix to echelon form and then to row reduced echelon form. Give the solution to the system in the form of a vector. Show that the coefficient matrix times the solution vector gives the right-hand side of the above system. Quiz 1 2. Consider the augmented matrix Page 2 of 2 1 l 1 -2 -1 3 3 -6 -2 2 Write the corresponding system of equations. Reduce the matrix to row reduced echelon form. Show all operations. Which are the pivot columns? Which is the free variable? Write the parameterized solution of the system using vector notation. Using the parameterized form you just computed, give a vector that is a particular solution for the above system. Show the vector solves the system. Also, using the parameterized form of the solution, give a vector that solves the homogeneous form of the above system, i.e., the above system with the right-hand side equal 0. Show the coefficient matrix times this vector is the 0 vector.

linear algebra

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