Get premium membership and access revision papers, questions with answers as well as video lessons.
Sma2113:Maths For Science Question Paper
Sma2113:Maths For Science
Course:Bachelor Of Computer Science
Institution: Meru University Of Science And Technology question papers
Exam Year:2013
QUESTION ONE (30 MARKS)
a) Differentiate between a vector quantity and a scalar quantity. (2 Marks)
b) Given that ?? = 4 3 7
and ?? =
3 -1 0
Find; i. ?? - ?? ii. ?? - ?? . (3 Marks) c) Given the points ?? 2,-1,3 ?????? ??(1,1,4). Find the distance between P and Q. (3 Marks)
d) If ?? ? 0 show that 1 ?? ??
is the unique unit vector in the same direction as ?? . (4 Marks) e) Given the following lines in parametric form; ?? = 3 + ?? ?? = 1 - 2?? ?? = 3 + 3?? ?????? ?? = 4 + 2?? ?? = 6 + 3?? ?? = 1 + ?? Determine their point of intersection. (4 Marks) f) Find the two points trisecting the line segment ?? 2,3,5 ?????? ??(8,-6,2). (4 Marks) g) Determine whether the vectors
?? =
1 0 -2 5 , ?? =
2 1 0 -1 and ?? = 1 1 2 1
are linearly independent in R4. (4 Marks)
2
h) Prove that the following transformation ??: R2 ? R2 is linear ?? ??,?? = (2??,?? + ??). (6 Marks)
QUESTION TWO (20 MARKS)
a) If ?? ,?? ?????? ?? are vectors in a vector space V. simplify 2 ?? + 3?? - 3 2?? - ?? - 3 2 2?? + ?? - 4?? - 4( ?? - 2?? )]. (4 Marks) b) Consider the vectors ??1 = 1 + ?? + 4??2 and ??2 = 1 + 5?? + ??2 in ??2. Determine whether ??1 and ??2 lie in the span 1 + 2?? - ??2,3 - 5?? + 2??2 . (10 Marks) c) Prove that the triangle inequality ?? + ?? = ?? + ?? holds for all vectors.(6 Marks)
QUESTION THREE (20 MARKS)
a) i) Let ?? and ?? be position vectors of two points A and B. if M is the point two thirds the way from A to B, show that the position vector ?? of M is given by ?? = 1 3 ?? + 2 3 ?? . (6 Marks) ii) Conclude that if ??(??1,??2,??3) and ??(??1,??2,??3) then M has coordinates ?? 1 3 ??1 + 2 3 ??1, 1 3 ??2 + 2 3 ??2, 1 3 ??3 + 2 3 ??3 . (4 Marks) b) show that the line through ??0(??0,??0 with slope M has direction vector ?? = 1 ?? and equation ?? - ??0 = ??(?? - ??0). (10 Marks)
QUESTION FOUR (20 MARKS)
A transformation is represented by the matrix ?? =
1 2 3 0 -1 1 1 1 4 , determine
i. The Kernel and its basis of the transformation. (10 Marks) ii. The range and its basis of the transformation. (10 Marks)
More Question Papers
Popular Exams
Return to Question Papers