Linear algebra

Topics: Linear algebra, Vector space, Determinant Pages: 2 (405 words) Published: October 22, 2014

KENYA METHODIST UNIVERSITY
END OF 3RD TRIMESTER 2012 (EVENING) EXAMINATIONS
FACULTY:SCIENCE AND TECHNOLOGY
DEPARTMENT:PURE AND APPLIED SCIENCES
UNIT CODE: MATH 110
UNIT TITLE:LINEAR ALGEBRA 1
TIME:2 hours
Instructions:
Answer question one and any other two questions.
Question One (30 marks)
Find the determinant of the following matrices.

-4 8 (2 marks)
0 1
1 -3 -2 (3 marks)
2 -4 -3
-3 6 +8
Find the values of x and y if:(5 marks)
x + 2y 14 = 4 14
-3 y-2 -3 7+3x
Solve the following simultaneous equations using matrix method. 3x + y = 4
4x + 3y = 7(5 marks)
Find the value of K which makes a singular matrix.(3 marks)
3 1
4 -2
4 K 0

Calculate the cross product of the vector U = 2i – 3j – k and V = i + 4j – 2k.(3 marks) Given the matrices.
2 5 3 -2 0
A = -3 1 and B = 1 -1 4
4 2 5 5 5
Compute:
ATB(3 marks)
tr (AB)(1 mark)

(e) Determine if (2, -1) is in the set generated by = (3, 1), (2, 2) (5 marks) Question Two (20 marks)
Let T: R2 R2 be defined by T(x, y) = (x + y, x). Show that T is a linear transformation.(7 marks) Find the basis and dimension of the row space of the matrix.(6 marks) 2 -1 3
A= 1 1 5
-1 2 2
Compute A-1 using row reduction method.(7 marks)

1 4 3
A= -1 -2 0
2 2 3
Question Three (20 marks)
Find x, y and z by use of determinants.(10 marks)
X – 3y – 2z – 6=0
2x – 4y – 3z – 8 =0
-3x + 6y + 8z + 5 =0

Determine S= (1, 0), (0, 1) if linearly independent or dependent. (3 marks)
Show that S= (1, 0, 0), (0, 1, 0), (0, 0, 1) is a basis for R3 (7 marks) Question Four (20 marks)
Consider the matrix
1 2 -3 1 2
A= 2 4 -4 6 10
3 6 -6 9 13
Reduce to an echelon form.
Reduce to its row canonical from.
State the rank of the...
Continue Reading

Please join StudyMode to read the full document

You May Also Find These Documents Helpful

  • Euclidian Algebra Essay
  • Linear Algebra Essay
  • Computer Linear Algebra Essay
  • Linear Algebra and Its Applications
  • Linear Algebra Problems Essay
  • Lights Out Linear Algebra Essay
  • Essay on Algebra 2
  • Essay about Linear Algebra and Score Student Number

Become a StudyMode Member

Sign Up - It's Free