Linear Algebra Answers

(Q3) Use Gaussian reduction to solve the following system of equations and verify your
results by using Mat Lab

X + Y + Z = 1
X + 2Y + 3Z = 2
2X + Y + 4Z = 5

Q1) Consider the square matrix A

{3,-1,0}
A= ,{-1,2-1},
{0,-1,3}
(i) Find the inverse of the matrix A.

(Q2) Find the solution to the following linear system by using
(i) Cramer rules
(ii) Inverse of matrix
(iii) Mat Lab with two different methods.

X + 2Y - Z = 2
3X + Y + Z = 4
X - Y + Z = 6

Solve the set of linear equations by Guassian elimination method : a+2b+3c=5, 3a-b+2c=8, 4a-6b-4c=-2. Find c

r4=r1+r2=r3,which of the vectors are linearly dependent?
a)r1
b)r3
c)r4
d)r2m

6 If A=2i−3j−k and B=i+4j−2k, find (A+B+×(A−B)
7 If A=3i−j+2k, B=2i+j−kand C=i−2j+2k, find (A×B)×C
8 Determine a unit vector perpendicular to the plane of A=2i−6j−3k and B=4i+3j−k
9 Evaluate (2i−3j)⋅[(i+j−k)×(3i−k)]
10 If A=i−2j−3k,B=2i+j−k and C=i+3j−2k,evaluate (A×B)⋅C

1 Find the angle between A=2x+2j−kand B=6i−3j+2k
2 Determine the value of a so that A=2i+aj+kand B=4i−2j−2k are perpendicular
3 Determine a unit vector perpendicular to the plane of A=2i−6j−3k and B=4i+3j−k
4 Find the work done in moving an object along a vector r=3i+2j−5k
5 Given that A=2i−j+3kand B=3i+2j−k, find A⋅B

A dot product is said to be distributive,if … …..

Solve the set of linear equations by the matrix method : a+3b+2c=3 , 2a-b-3c= -8, 5a+2b+c=9. Sove for a

Let B = far a2, a3) be an ordered basis of
R3 with al = (1, 0, -1), a2 = (1, 1, 1),
a3 = (1, 0, 0). Write the vector v = (a, b, c) as
a linear combination of the basis vectors
from B.
(b) Suppose al = (1, 0, 1), a2 = (0, 1, -2) and
a3 = (-1, -1, 0) are vectors in R3 and
f : R3 -> R is a linear functional such that
f(al) = 1, f(a2) = -1 and f(a3) = 3. If
a = (a, b, c) E R3, find f(a).