Exercises on elimination with matrices
Problem 2.1: In the two-by-two system of linear equations below, what multiple of the first equation should be subtracted from the second equation when using the method of elimination? Convert this system of equations to matrix form, apply elimination (what are the pivots?), and use back substitution to find a solution. Try to check your work before looking up the answer.
2x + 3y = 5
6x + 15y = 12
Problem 2.2: (2.3 #29. Introduction to Linear Algebra: Strang) Find the triangular matrix E that reduces “Pascal’s matrix” to a smaller Pascal:
1 1 0 0 0 1 0 0 ⎥
E 0 0 1 1 0 ⎥ .
1 3 3 1 0 1 2 1
Which matrix M (multiplying several E’s) reduces Pascal all the way to I?
