sample_tt1_2

# sample_tt1_2 - Math 136 Sample Term Test 1 2 NOTES...

This preview shows pages 1–2. Sign up to view the full content.

Math 136 Sample Term Test 1 - 2 NOTES: - Questions 7, 10b on this test cover material that will not be covered on our term test 1. 1. Short Answer Problems a) State the deﬁnition of the rank of a matrix. b) What can you say about the consistency and the number of parameters (free variables) in the general solution of a system of 5 linear equations in 4 variables. c) Let A = ± 3 2 1 - 2 1 4 ² and B = - 2 1 1 1 0 - 1 . Calculate AB . d) Let S = { ~v 1 ,~v 2 ,~v 3 } be a set of vectors in R 3 . State the deﬁnition of the set S being linearly independent. e) Give an example of vectors ~u and ~v in R 3 such that the vector equation ~x = s~u + t~v , s,t R , is not a plane. 2. Consider the system of linear equations: - 2 x + 3 y + 3 z = - 9 3 x - 4 y + z = 5 - 5 x + 7 y + 2 z = - 14 a) Write the augmented matrix and row reduce it to RREF using elementary row operations. b) What is the rank of the coeﬃcient matrix? c) Find the general solution of the system.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 2

sample_tt1_2 - Math 136 Sample Term Test 1 2 NOTES...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online