2. The goal is to compute the determinant of the following matrix. Follow the instructions. 2 -3 7 -1 3 0 -4 A = 2 -8 3 5 -2 7 Expand det(A) using column 3. You should have two 3 x 3 determinants in your set-up. Compute the two 3 × 3 determinants in your set-up. Check the answer key first. Plug in your answers to (b) to complete the computation of det(A). а. b. с.
Addition Rule of Probability
It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.
Expected Value
When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).
Probability Distributions
Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.
Basic Probability
The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.
7.3 #2
The question is in the picture please answer a, b and c
![### Computing the Determinant of a Matrix
The aim is to compute the determinant of the following 4x4 matrix \(A\). Follow these instructions to complete the task.
#### Matrix \(A\):
\[
A = \begin{pmatrix}
2 & -3 & 7 & 2 \\
-1 & 3 & 0 & -4 \\
2 & -8 & 0 & 3 \\
6 & 5 & -2 & 7
\end{pmatrix}
\]
#### Steps:
**a. Expand \(\text{det}(A)\) using column 3. You should have two 3x3 determinants in your set-up.**
**b. Compute the two 3x3 determinants in your set-up. Check the answer key first.**
**c. Plug in your answers to (b) to complete the computation of \(\text{det}(A)\).**
### Detailed Instructions:
1. **Expanding Determinant Using Column 3:**
To expand the determinant of matrix \(A\) using its third column, consider the elements in the third column and their corresponding minors (3x3 matrices obtained by deleting the row and column that contain each element).
2. **Calculating the Resulting 3x3 Determinants:**
Compute the two 3x3 determinants that result from the expansion.
3. **Final Computation:**
Use the results of the two 3x3 determinants to find the determinant of the original 4x4 matrix \(A\).
This process involves using the method of cofactor expansion, often referred to as Laplace expansion, to reduce the computation of a 4x4 determinant to the computation of several 3x3 determinants.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcecab317-fab7-42bc-8c65-e82787a88e59%2Fd829b5ac-6d14-41ad-9bb9-a56d732b9620%2F531kdvg_processed.png&w=3840&q=75)
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