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Possible Value - Linear Algebra - Exam, Exams of Linear Algebra

Amity University - BiharLinear Algebra

This is the Past Exam of Linear Algebra which includes Row Equivalent, Scalars, Column Vectors, Components, Values, System of Equations, Matrix Equation, Represented, Special Conditions etc. Key important points are: Possible Value, Equations, Augmented Matrix, System, Solution, Calculations, Invertible, Matrices, Columns, Vectors

Typology: Exams

2012/2013

Uploaded on 02/27/2013

sekar_53
sekar_53 🇮🇳

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Math 205A Test 1 (50 points)
Name:
•Check that you have 8 questions on three pages.
•Show all your work to receive full credit for a problem.
1. (5 points) (For this problem do all calculations by hand.) The augmented matrix of a system
of equations is given below. Find all possible value(s) of hso that the system has a solution.
1h2
254
2. (5 points) Suppose A,B,Cand Xare invertible n×nmatrices and A(X+B)T=CA. Solve
for X.
pf3
pf4
pf5

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Math 205A Test 1 (50 points)

Name:

  • Check that you have 8 questions on three pages.
  • Show all your work to receive full credit for a problem.
  1. (5 points) (For this problem do all calculations by hand.) The augmented matrix of a system of equations is given below. Find all possible value(s) of h so that the system has a solution. [ 1 h 2 2 5 4

]

  1. (5 points) Suppose A, B, C and X are invertible n × n matrices and A(X + B)T^ = CA. Solve for X.
  1. (6 points) Let A be a matrix such that its columns are vectors in R^6. The general solution of the equation A~x = ~0 is as follows.

x 1 = 2 x 3 − x 5 x 2 = x 3 + x 5 x 4 = 3 x 5 x 3 , x 5 are free

(a) Are the columns of A linearly independent? Explain.

(b) Do the columns of A span R^6? Explain.

  1. (10 points) Let A =

. Let T be a linear transformation given by T (~x) = A~x

(a) Describe the vectors in Nul A in parametric vector form.

(b) Is T one-to-one? Explain.

(c) Find three distinct non-zero vectors in Col A.

  1. (5 points) Let T : R^3 → R^2 be a transformation such that

T (x 1 , x 2 , x 3 ) = (9x 3 − x 1 , 4 x 2 x 3 + x 1 ).

Is T a linear transformation? Explain.

  1. (5 points) Let H =

b + d a − d a − 2 c + d c + 3d

 :^ a, b, c, d^ are real numbers.

Is H a subspace of R^4? Explain.