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Quiz 1: Linear Algebra and Probability
Test your knowledge on fundamental concepts of Linear Algebra and Probability.
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1. What is the result of adding two vectors?
A scalar
A vector
A matrix
A tensor
2. Which operation calculates the magnitude of projection of one vector onto another?
Cross product
Dot product
Vector addition
Scalar multiplication
3. What is the determinant of a matrix used for?
Calculating the inverse of the matrix
Determining if the matrix is invertible
Finding eigenvalues
All of the above
4. In probability, what does a 'sample space' refer to?
The set of all possible outcomes
The set of all favorable outcomes
The set of all impossible outcomes
The set of all independent events
5. What is conditional probability?
The probability of an event occurring given that another event has occurred
The probability of two independent events occurring simultaneously
The probability of an event not occurring
The probability of all possible outcomes
6. Which theorem relates conditional probability to its reverse condition?
Law of Large Numbers
Central Limit Theorem
Bayes' Theorem
Pythagorean Theorem
7. What does the mean represent in descriptive statistics?
The middle value in a dataset
The most frequently occurring value
The average of all values
The difference between the maximum and minimum values
8. Which measure indicates the spread of data in a dataset?
Mean
Median
Mode
Standard deviation
9. What type of distribution is characterized by a bell-shaped curve?
Uniform distribution
Normal distribution
Poisson distribution
Exponential distribution
10. In matrix operations, what is the result of multiplying a matrix by its inverse?
A zero matrix
An identity matrix
A diagonal matrix
A scalar matrix
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