Question

Multiple choice

1. if a = [1, 2] b = [2, 7] find a + 2b

A.3 √10 B. [6, 18] C. [5, 16] D. √281

2. if p = [ 5, -3] and q = [ 1, 4] find |p - 51|

a. [0, 23] b. 23 c. 529 d. [4, -7]

3. if a = [ 5, -5] and b = [-5, 5] find A x B (A multiply by B)

a. 50 b. 0 c. -50 d. 625

4. if a = [5, -4, 3] and b = [-2, 3, k] find k such that a and b are orthogonal

a. 1 b. 3 c. 7 d. 22/3

5. Which vector is collinear with [2, -3]

a. [2, -6] b. [-2, -3] c. [12, 18] d. [-4, 6]

Answer #1

a = [-5, -3, 2] b = [1, -7, 9] c = [7, -2, -3] d = [4, -1, -9,
-3] e = [-2, -7, 5, -3]
a. Find (d) (e)
b. Find (3a) (7c)
c. Find Pe --> d
d. Find Pc --> a +2b
ex. C = |x|(xy/xy) C = xy/|x|
ex. P x --> y = Cux = C(xy/x) (1/|x|) (x) =( xy/yy)(y)

#2. For the matrix A = 1 2 1 2 3 7 4 7 9 find the
following. (a) The null space N (A) and a basis for N (A). (b) The
range space R(AT ) and a basis for R(AT )
. #3. Consider the vectors −→x = k − 6 2k 1 and −→y =
2k 3 4 . Find the number k such that the vectors...

Find regression line for the data
X 0 1 2 3
4 5 6 7
8
Y 11 21 31 41 51 61 71 81 91
X 0 2 4 6 8
10
Y 12 15 17 18 20 22

1. Compute the angle between the vectors u = [2, -1, 1] and and
v = [1, -2 , -1]
2. Given that : 1. u=[1, -3] and v=[6, 2], are u and v
orthogonal?
3. if u=[1, -3] and v=[k2, k] are orthogonal vectors.
What is the
value(s) of k?
4. Find the distance between u=[root 3, 2, -2] and v=[0, 3,
-3]
5. Normalize the vector u=[root 2, -1, -3].
6. Given that: v1 = [1, - C/7]...

2. Write the output matrix “v”
t = [2:4];
k = [1:3];
v = t.*k – k.^2
4. Given: D = [1 2 3 4 5 6 7 8 9] (3x3) . Which command will
extract the submatrix [1 2 3 4 5 6] (2x3) ?
a. D[1:2,1:3]
b. D(1,2 ;1,3)
c. [D(1:2),D(1:3)]
d. D(1:2,1:3)
14. What will be the dimension of matrix B?
B=[ones(3) zeros(3) rand(3); 2*eye(9)]
18. Find the value of “C”
A=1:2:10;
B=linspace(1,5,5);
C = length(A)*B(2)+A(5)*B(3);
19....

Let p = (8, 10, 3, 11, 4, 0, 5, 1, 6, 2, 7, 9) and let q = (2,
4, 9, 5, 10, 6, 11, 7, 0, 8, 1, 3) be tone rows. Verify that p =
Tk(R(I(q))) for some k, and find this value of k.

3) If A = 3
1 and B
= 1 7
0
-2
5 -1
Find
a) BA
b) determinant
B
c) Adjoint A
d)
A-1
4) Using matrix method solve the following simultaneous
equations
5x – 3y = 1
2x – 2y = -2
5) Given that f(x) = 6x - 5 g(x) = 3x +
4 and h(x) = 4x – 6
2
Find:-
i)...

x y s t P
1 -3 1 0 0 12
1 2 0 1 0 3
-6 -4 0 0 1 0
The pivot element for the initial simplex tableau show is the
red 1. So we need to zero out the other elements of column x. What
is the formula used to zero out row 1 and column x?
Multiply Row _____by_______ and then
add the result to Row_____
What is the formula used to zero out row...

Refer to the following matrices.
A =
1
−8
7
−3
−18
6
5
8
6
0
5
8
3
4
8
−2
B =
4
−7
4
0
1
4
9
5
3
−3
0
9
C =
1
0
3
2
8
D =
1
9
−7
0
What is the size of each matrix?
A
____× ____
B
_____× _____
C
____× ____
D
____× _____

Consider a TSP case with 9 cities to be visited (starting from D
and returning to D). Using the distance matrix is provided below,
use the nearest neighborhood heuristic to find the minimum distance
route.
Distances
D
1
2
3
4
5
6
7
8
D
0
61
42
22
50
45
32
57
30
1
61
0
21
62
80
91
32
76
82
2
42
21
0
41
61
71
20
71
67
3
22
62
41
0...

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