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3 years ago

If Matrix A has dimensions 2 x 2, and Matrix B has dimensions 3 x 2, can Matrix A and Matrix B be multiplied?

1 answer:

5 0

In order for two matrices A and B to be multiplied, they should be conformable. The columns of A should match the rows of B.

Given:
A is (2 x 2) => rows = 2, columns =2
B is (3 x 2) => rows = 3, columns = 2

Because 2 (columns of A) is not equal to 3 (rows of B), the matrices cannot be multiplied because they are not conformable.

Answer:
A and B cannot be multiplied.

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Suppose that bugs are present in 1% of all computer programs. A computer de-bugging program detects an actual bug with probabili

lawyer [7]

Answer:

(i) The probability that there is a bug in the program given that the de-bugging program has detected the bug is 0.3333.

(ii) The probability that the bug is actually present given that the de-bugging program claims that bugs are present on both the first and second tests is 0.1111.

(iii) The probability that the bug is actually present given that the de-bugging program claims that bugs are present on all three tests is 0.037.

Step-by-step explanation:

Denote the events as follows:

B = bugs are present in a computer program.

D = a de-bugging program detects the bug.

The information provided is:

$P(B) =0.01\\P(D|B)=0.99\\P(D|B^{c})=0.02$

(i)

The probability that there is a bug in the program given that the de-bugging program has detected the bug is, P (B | D).

The Bayes' theorem states that the conditional probability of an event E given that another event X has already occurred is:

$P(E|X)=\frac{P(X|E)P(E)}{P(X|E)P(E)+P(X|E^{c})P(E^{c})}$

Use the Bayes' theorem to compute the value of P (B | D) as follows:

$P(B|D)=\frac{P(D|B)P(B)}{P(D|B)P(B)+P(D|B^{c})P(B^{c})}=\frac{(0.99\times 0.01)}{(0.99\times 0.01)+(0.02\times (1-0.01))}=0.3333$

Thus, the probability that there is a bug in the program given that the de-bugging program has detected the bug is 0.3333.

(ii)

The probability that a bug is actually present given that the de-bugging program claims that bug is present is:

P (B|D) = 0.3333

Now it is provided that two tests are performed on the program A.

Both the test are independent of each other.

The probability that the bug is actually present given that the de-bugging program claims that bugs are present on both the first and second tests is:

P (Bugs are actually present | Detects on both test) = P (B|D) × P (B|D)

$=0.3333\times 0.3333\\=0.11108889\\\approx 0.1111$

Thus, the probability that the bug is actually present given that the de-bugging program claims that bugs are present on both the first and second tests is 0.1111.

(iii)

Now it is provided that three tests are performed on the program A.

All the three tests are independent of each other.

The probability that the bug is actually present given that the de-bugging program claims that bugs are present on all three tests is:

P (Bugs are actually present | Detects on all 3 test)

= P (B|D) × P (B|D) × P (B|D)

$=0.3333\times 0.3333\times 0.3333\\=0.037025927037\\\approx 0.037$

Thus, the probability that the bug is actually present given that the de-bugging program claims that bugs are present on all three tests is 0.037.

4 0

3 years ago

1. Renting a bicycle at a local Bike shop costs $30 for the first day and $10 for each additional day.

r-ruslan [8.4K]

(a) d=days C=cost

d C
1 30
2 40
3 50
4 60

C=10(d-1)+30

(b) C=10(5-1)+30
C=40+30
C=70

7 0

3 years ago

What is the next term in the number pattern? 21, 31, 36, 46, 51, … Enter your answer in the box.

Leni [432]

Answer:

Step-by-step explanation:

first it goes up by 10 then 5 now 10

7 0

3 years ago

Read 2 more answers

The lengths in cm, of the sides of a triangle are 3x - 5, 2x-1 and x+1

Dennis_Churaev [7]

Answer:

a) p = 6x - 5

b) x = 6

Step-by-step explanation:

a) p = a + b + c

p = 3x - 5 + 2x - 1 + x + 1

p = 6x - 5

b) p = 6x - 5 =31

6x - 5 = 31

6x = 36

x = 6

3 0

3 years ago

What is the number called next to the variable?

Schach [20]

Answer:

The number next to a variable is called the Coefficient of the variable.

7 0

4 years ago

Read 2 more answers