{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

exam2_sl

# exam2_sl - M341 Midterm Exam 2 56215 Solution I(20 points...

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

M341 Midterm Exam 2 56215 Solution I. (20 points) Mark the following statements either "True" or "False". Circle T for true and F for False. No proof or explanation is needed. 1. (T) If A , B are nonsingular n × n matrices, then (( AB ) T ) 1 = ( A 1 ) T ( B 1 ) T . 2. (F) The inverse of a type (I) row operation is a type (II) row operation. 3. (F) Span ( S ) is only de ned if S is a nite subset of a vector space. 4. (T) An n × n matrix A has determinant zero if and only if rank ( A ) < n . 5. (F) The set of all polynomial of degree 7 is a vector space under the usual operations of addition and scalar multiplication. 6. (F) Any plane W in R 3 is a subspace of R 3 under the usual operations. 7. (F) The set of all vectors of the form [0 , a, b, 1] is a subspace of R 4 under the usual operations. 8. (F) Let W 1 and W 2 be two subspaces of a vector space V . Then their union W 1 ∪ W 2 is also a subspace of V . 9. (T) If two rows of a square matrix A are identical, then | A | = 0 . 10. (T) If x is a linear combination of the rows of A , and B is row equivalent to A , then x is in the row space of B . II. Rank 1. (3 points) Give the de nition of the rank of a matrix A . Ans: The rank of a matrix A is the number of nonzero rows in the unique reduced row echelon form that is row equivalent to A . 2. (4 points) Let A and B be two matrices as following: A = 1 2 0 0 3 2 5 3 2 6 0 5 15 10 0 2 6 18 8 6 , B = 0 2 7 5 0 0 1 3 2 0 1 2 1 0 3 2 6 18 10 6 Find the rank of A and B .

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 / 4

exam2_sl - M341 Midterm Exam 2 56215 Solution I(20 points...

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

View Full Document
Ask a homework question - tutors are online