Linear Algebra Answers

solve gauss elimination

(1) w-x+3y-3z=3 (2) 3x1+2x2+x3=3
2w-3x+y-11z=1 2x1+x2+x3=0
5w-2x+5y-4z=5 6x1+2x2+4x3=6
3w+4x-7y+2z=-7

1 Solve the set of linear equations by Guassian elimination method : a+2b+3c=5, 3a-b+2c=8, 4a-6b-4c=-2. Find c
1
5
4
10

2 Solve the set of linear equations by the matrix method : a+3b+2c=3 , 2a-b-3c= -8, 5a+2b+c=9. Sove for b
9
-3
5
-4

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

4 Solve the set of linear equations by Guassian elimination method : x+2y+3z=5, 3x-y+2z=8, 4x-6y-4=-2. Find a
-1
4
5
-11

5 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
2
4
7
3

6 For a relation R in A. if , then R is a ______ relation.
transitive
reflexive
symmentric
associative

7 For a relation R in A.[Math Processing Error],it implies that a =b, then R is an ______ relation.
associative
anti- symmetric
complex
transitive

Check sings definiteness
Y=f(X1, X2) =2X12- 4X1X2+3X22

Find all possible matrix products of two different matrices among the three
matrices below.

A = -1, 3, 4
0, -2, 5

B= -2, 4, 3
-1, -4, 2
2, 4, 3

C= -3, 2
-1, 6

Find a basis for the subspace W of R4, spanned by the set of vectors V1 {[1 1 0 -1]}, V2 {[0 1 2 1]}, V3 {[1 0 1 -1]}, V4 {[1 1-6 -3]}
and V5 {[-1 -5 1 0]}

What is the dimension of W?
Let W be the subspace of P3 spanned by:
{t^3 + t^2 -2t +1 , t^2 + 1 , t^3 - 2t , 2t^3 +3t^2 -4t +3}.
Find a basis for W. What is the dimension of w?

If Ax =tx
Where t = 2 2 -2
1 3 1
1 2 1
Determine the eigen values of the matrix A, and an eigen vector corresponding to each eigen value. If t = 4

Coplanarity of three vectors a, b, c is known as ……………
dependent
independent
linearly dependent
linearly independent

Let
A=2i−j+k
,
B=i+3j−2k
,
C=−2i+j−2k
and
D=3i+2j+5k
. Find scalar a, b, c such that
D=aA+bB+cC

a=−1,b=1,c=2

a=5,b=1,c=1

a=−2,b=1,c=−3

a=−1,b=1,c=2

6 Compute the determinant of :
∣∣∣−2−314∣∣∣
5
-5
4
-4

7 Compute the determinant of :
∣∣∣−1−4−1−2∣∣∣
8
4
3
-2

8 Two systems of linear equations involving the same variables are said to be _______ if they have the same solution set.
set
associative
equivalent
parallel

9 A + (B + C)= (A + B) + C
associative
scalar quantity
dot product
2

10 A + B = B + A
associative
m
commutative
m-n

1 Consider a 3x3 square matrix given as
⎡⎣⎢200020001⎤⎦⎥
. What is the element in
a22
2
0
1
0,0

2 A + B = B + A
associative
m
commutative
m-n

3 Find z by the use of determinant : 3x-4y+2z+8=0, x+5y-3z+2=0, 5x+3y-z+6=0
6
7
3
5

4 Find x by the use of determinant : 3x-4y+2z+8=0, x+5y-3z+2=0, 5x+3y-z+6+0
3
5
2
-2

5 Compute the determinant using elements in the first row:
A∣∣∣∣1540−7−8371∣∣∣∣
-7
32
13
3