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Linear Algebra Examination 2 - Mr. Haines, Exams of Linear Algebra

Bidhan Chandra Krishi ViswavidyalayaLinear Algebra

The second examination of mathematics 205 - linear algebra, taught by mr. Haines. The exam covers various topics such as finding subspaces, bases, determinants, and dimensions. It includes multiple-choice questions and problems that require finding the basis of a matrix, calculating determinants, and determining the rank of a matrix.

Typology: Exams

2012/2013

Uploaded on 02/27/2013

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sehgal_98 🇮🇳

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NAME_______________________________________
I___II___III___IV___V___VI___VII___VIII___ IX___X___XI___TOTAL ___________
October 27 Mathematics 205 Mr. Haines
2004 Linear Algebra
Examination #2
(10) I. Suppose A =
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A. If col A is a subspace of m
ℜ, what is the value of m ?
B. If nul A is a subspace of m
ℜ, what is the value of m ?
(5) II. Give an example of a two-dimensional subspace of 4
ℜ. Use correct mathematical
notation to describe it.
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NAME_______________________________________

I___II___III___IV___V___VI___VII___VIII___ IX___X___XI___TOTAL ___________

October 27 2004 Mathematics 205Linear Algebra Mr. Haines Examination #

(10) I. Suppose A =  

A. If col A is a subspace of ℜ m , what is the value of m?

B. If nul A is a subspace of ℜ m , what is the value of m?

(5) II. Give an example of a two-dimensional subspace ofnotation to describe it. ℜ 4. Use correct mathematical

(20) III. If A = 

A. Find a basis for Col A.

B. Find a basis for Nul A.

C. What is the dimension of Col A?

D. What is the dimension of Nul A?

E. What is the rank of A?

(5) VI. Suppose that B is obtained from A by interchanging the first two rows of A, and that det (A) = det (B). What is the value of det (A)?

(5) VII. Give an example of a matrix A whose null space, Nul A, is a straight line in ℜ 3.

(10) VIII. Compute the area of the parallelogram whose vertices are the points (4, 5), (1, 1), (2, 4), and (3, 2).

(10) IX. Suppose AB = (^) ^14 7 − 32 and B = (^)  07 10 . Find A.