# Past Exam for 1016 331 - Linear Algebra I at RIT (RIT)

## Exam Information

 Material Type: Exam 2 Professor: Staff Class: 1016 331 - Linear Algebra I Subject: Mathematics & Statistics University: Rochester Institute of Technology Term: 2009 Keywords: Possible ValueFollowing MatrixTransformationColumn Space

## Sample Document Text

1016-331 RIT, 20091 1 Linear Algebra I 1016-331 Test 2 Solution 1. (6p) We know that the following matrix A has the reduced row echelon form R: A = 2 4 1 2 ¡3 ¡4 ¡2 ¡4 7 9 1 2 ¡6 ¡7 3 5; 2 4 1 2 0 ¡1 0 0 1 1 0 0 0 0 3 5 = R: (a) Find a basis for row(A). The nonzero rows from R: f£ 1 2 0 ¡1 ?;£ 0 0 1 1 ?g (b) Find a basis for col(A). The pivot columns from A: f 2 4 1 ¡2 1 3 5; 2 4 ¡3 7 ¡6 3 5g (c) Find a basis for null(A). We solve the system given by Ax = 0: if the variables are x;y;z and u, then from R we see that y and u are free and z = ¡u and x = u¡2y. This means that the solutions are 2 66 4 x y z u 3 77 5 = 2 66 4 u¡2y y ¡u u 3 77 5: This shows that the answer is f 2 66 4 ¡2 1 0 0 3 77 5; 2 66 4 1 0 ¡1 1 3 77 5g 1016-331 RIT, 20091 2 2. (6p) Find the dimension of spanf 2 66 4 1 2 ¡3 ¡4 3 77 5; 2 66 4 ¡2 ¡4 7 9 3 77 5; 2 66 4 1 2 ¡6 ¡7 3 77 5g: This span is just the row space of the previo...