Evaluation File: 1306805

Solution 1

• Correct ( Use [ ] bracket instead of ( ))

Solution:

A =

B =

AB =

AB =

• (i) Correct but formatting error

Solution:

4x +2y = 14    ……………..(1)

2x-y =1……………………..(2)

Multiply with 2 in equation (2)

4x -2y =2……………….equation (3)

Addition of equation 2 and equation 3;

4x +2y = 14    

4x -2y =2

• +      –

——————-

4y = 12

y = 12/4

y = 3

Substituting the value of y in equation (2);

2x-3 =1

2x = 4

x = 4/2 = 2

(ii) Correct but formatting error

Solution:

Given Matrix,

M =

∆ = (4 ×-1) – (2× 2) = -4-4 = -8

^-1 =   =

(iii) Incorrect, you selected incorrect matrix in N

Solution:

M^-1 =

N =

M^-1 N =  =

Solution 3

• Incorrect, the vector will be added rather than subtracted.

Solution:

 = i +j +2k

 = 4i +5j +7k

Resultant = 5i +6j +9k

Magnitude =  = 10.4880

• Incorrect, due to wrong resultant

Only change the resultant with 5i +6j +9k

Solution:

r = a + λm

r = I +j +2k +λ (5i +6j +9k)

Parametric form:

r = i+j +2k +λ (5i +6j +9k)

x = 1+5 λ

y = 1+6 λ

z = 2+9 λ

Cartesian form:

x = 1+5 λ

λ = (x-1)/5

y = 1+6 λ

λ = (y-1)/6

z = 2+9 λ

λ = (z-2)/9

(x-1)/5 = (y-1)/6 = (z-2)/9

•  Incorrect, due to wrong resultant

Only change the resultant with 5i +6j +9k

Solution:

r₁ = i+j +2k +λ (5i +6j +9k)

r₂ = i+j +2k +λ (2i +2j -3k)

The gradient is different, hence intercept

a.b = (5×2) +(6 ×2) + (9×-3)

a.b = -5

-5 =  cos

-5 = 10.4880. cos

2.0677⁰

Solution 4

• (i) Correct

(ii) Correct

(iii) Correct

• Incorrect, in third line you missed the square of y, please mention 2y² instead of 2y at every below lines.

Solution:

 = [ 2xy² + 2x³]₀¹

 = [2y² +2] – [0+0]

= [2y² +2]

= [ (2y³/3) + 2y]₁²

= [ (2(2)³/3) + 2×2] – [(2/3)+2]

= 20/3

Solution 5

• Incorrect, Do the first part (AB) in similar way as (BA)

Solution:

A =

B =

AB  = [8+21]

AB  = [29]

• Correct
• Correct
• Incomplete solution, Do another part (b) by mentioning the value in formula.

Solution:

P(AUB) = P(A) + P(B) – P(A intersection B)

P(AUB) = 0.5 +0.5 – 0.25

P(AUB) = 0.75