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9 Questions for Exam 2 - Elementary Linear Algebra | MATH 204, Exams of Algebra

Material Type: Exam; Class: Elementary Linear Algebra; Subject: Mathematics; University: Western Washington University; Term: Spring 2006;

Typology: Exams

Pre 2010

Uploaded on 08/16/2009

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MATH 204 Test 2
April 28, 2006 Name
Put your answers in the space provided. Show your reasoning. The maximum score on the test is 30 points.
1. 4 points Let A=
5 1 4
6 1 5
7 1 6
,
1a. Explain why Ais singular.
1b. Construct a non-zero, 3×3matrix Bfor which AB = 0. Note: Bmay have zero entries but
not all the entries in Bare zero. Circle your answer.
2. 4 points Consider the linear transformation T:R2R2which maps e1to e12e2and maps the vector
e2to twice e2. Find the standard matrix of T.Circle your answer.
pf3
pf4

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MATH 204

Test 2 April 28, 2006 Name

Put your answers in the space provided. Show your reasoning. The maximum score on the test is 30 points.

  1. 4 points Let A =

  

  ,

1a. Explain why A is singular.

1b. Construct a non-zero, 3 × 3 matrix B for which AB = 0. Note: B may have zero entries but not all the entries in B are zero. Circle your answer.

  1. 4 points Consider the linear transformation T : R^2 → R^2 which maps e 1 to e 1 − 2 e 2 and maps the vector e 2 to twice e 2. Find the standard matrix of T. Circle your answer.
  1. 2 points Complete the following definition: A set of vectors is said to be a basis for a subspace H of Rn^ if
  2. 3 points Solve the equation (A + BX)C = D for X, assuming that A, B, and C are n × n invertible matrices. Circle your answer
  3. 4 points Find the inverse of the matrix A =

 

 . Show the appropriate steps for computing A− 1

without using your calculator. Circle your answer.

  1. 2 points Complete the following definition: A set of vectors is said to be a basis for a subspace H of Rn^ if
  2. 4 points Consider the following five vectors in R^3 :

a 1 =

 

  , a 2 =

 

  , a 3 =

 

  , a 4 =

 

  , b =

 

 .

They are the columns of the following matrix [A b] and the matrix R is its row reduced echelon form:

[A b] =

 

  R =

 

 

9a Find a basis for Nul(A). Circle your answer.

9b. Find a basis for Col(A). Rectangle your answer.