Multivariate MCQs – 1

1. Let $A$ be a $k\times k$ symmetric matrix and $X$ be a $k\times 1$ vector. Then

2. If $A$ is a square matrix, then $det(A – \lambda)=0$ is known as

3. A square matrix $A$ and its transpose have the Eigenvalues

4. Eigenvalue often introduced in the context of

5. Let $x_1, x_2, \cdots, x_n$ be a random sample from a joint distribution with mean vector $\mu$ and covariance $\sigma$. Then $\overline{x}$ is an unbiased estimator of $\mu$ and its covariance matrix is:

6. A set of vectors $X_1, X_2, \cdots, X_n$ are linearly independent if

7. The pdf of multivariate normal distribution exists only when $\sigma$ is

8. Length of vector $\underline{X}$ is calculated as

9. The set of all linear combination of $X_1, X_2, \cdots, X_k$ is called

10. Eigenvalue is the factor by which the Eigenvector is

11. Let $x_1, x_2, \cdots, x_n$ be a random sample of size $n$ from a p-variate normal distribution with mean $\mu$ and covariance matrix $\sigma$, then

12. Let $x$ be distributed as $N_p(\mu, \sigma)$ with $|\sigma | > 0$, then $(x-\mu)’ \sigma^{-1} (x-\mu)$ is distributed as:

13. If $A$ and $B$ are two $n \times n$ matrices, which of the following is not always true?

14. If $A$ is a square matrix of order ($m \times m$) then the sum of diagonal elements is called

15. Eigenvalues and Eigenvectors are only for the matrices

16. How many Eigenvalues does a 2 by 2 matrix have?

17. What are Eigenvalues?

18. A matrix in which number of rows and columns are equal, is called

19. The rank of a matrix $\begin{bmatrix}1 & 0 & 1 & 0 & 2 \\ 0 & 0 & 1 & 1 & 2 \\ 1 & 1 & 0 & 0 & 2 \\ 0 & 1 & 1 & 1 & 3\end{bmatrix}$ is

20. A matrix $A_{m\times n}$ is defined to be orthogonal if\choice{$A’A=I$}{$A^{-1}=A’I$}{$A’A = AA’=I$}{All given Options}{d}{}