Linear Algebra Answers

1 A ……... is a rectangular array of numbers that are enclosed within a bracket .
horizontal
set
vertical
matrix

2 When the numbers of rows is equal to the numbers of columns equal to 'n'. Where m=n. Then is called…..
a square matrix
a column
a row
a matrix

3 What is this matrix called :
[0000]
diagonal matrix
proper matrix
zero matrix
square matrix

4 What is another name given to an identity matrix
unit matrix
diagonal matrix
special matrix
triangular matrix

5 Let A be a
n×n
square matrix . A is a symmetric matrix if A equal to …….
AT
B
C
4BT

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
4
5
9
10

7 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

8 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

9 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

10 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

1 Solve for x and y: 3x + 4y = 9, 2x + 3y =8
x = 7.5, y = - 4. 5
x = 7.0, y = - 4. 5
x = 4.5, y = - 7. 5
x = 7.5, y = - 4. 1

2 If A.x=
λx
,where A=
∣∣∣∣211232−212∣∣∣∣
,determine the eigen values of the matrix A, and an eigen vector corresponding to each eigen value. If
λ=2
,what is b
{0,1,0}
{3,0,2}
{2,0,1}
{0,1,1}

3 If A.x=
λx
,where A=
∣∣∣∣211232−212∣∣∣∣
,determine the eigen values of the matrix A, and an eigen vector corresponding to each eigen value. If
λ=4
,what is c
{2,3,0}
{-2,1,1}
{2,1,1}
{3,2,6}

4 Solve the set of linear equations by the matrix method : a+3b+2c=3 , 2a-b-3c= -8, 5a+2b+c=9. Sove for c
5
1
2
7

5 If A.x=
λx
,where A=
∣∣∣∣211232−212∣∣∣∣
,determine the eigen values of the matrix A, and an eigen vector corresponding to each eigen value. If
λ=1
,what is a
{-2,1,0}
{3,5,2}
{1,0,0}
{2,1,4}

Let V be a vector space over a field F and function
I:V→V
be the identity transformation. Find range of I R(I)

: Given matrices A, B, and C, below, preform the indicated operations if possible. If the operation is not possible, explain why.

[2 -1 0 ] [5 0 2 ]
A= [0 5 0.3] B= [1 -3 9] C= [1 3 5]
[1 4 10 ] [2 0 4 ]

a. 3A + B

b. 2B + C

c. CA

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
4
5
9
10

7 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

8 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

9 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

10 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

1 Solve the equations 5x + 2y = 14, 3x - 4y - 24.
x = 4, y = -4
x = 4, y = -2
x = 4, y = -3
x = 4, y = 3
2 Solve the linear equation 2x+3y=1, 5x+7y=3.
x=2, y=-1
x=4, y=-2
x=2, y=-2
x=5, y=-3
3 Solve the linear equations 2x+4y=10 and 3x+6y=15.
x=5-2a,y=a
x=5-2a,y=4
x=5,y=a
x=-2a,y=a
4 Solve the set of linear equations by the matrix method : a+3b+2c=3 , 2a-b-3c= -8, 5a+2b+c=9. Sove for c
3
1
5
7
5 Solve the linear equation : 2x+3y=3, x-2y=5 and 3x+2y=7.
x=2 and y=-1
x=3 and y=1
x=3 and y=-1
x=1 and y=-1

Solve the linear equation : 2x+y-3z= 5,3 x-2y-2z= 5, and 5x-3y-z= 16.

Let C=
5 4 -8
11 -9 17
6 -5 10
be a matrix of cofactors of matrix A, then the adjoint of A will be .......

Whichofthefollowingstatementsaretrueandwhicharefalse?Justifyyouranswerwitha shortprooforacounterexample. .2)Theoperation∗definedbyx∗y=log(xy)isabinaryoperationonS,whereSisthe set{x∈R|x>0}.