CMI-2018-DataScience-A: 3

Question

Let $x=\begin{bmatrix} 3& 1 & 2 \end{bmatrix}$. Which of the following statements are true?

• A. $x^Tx$ is a $3\times 3$ matrix
• B. $xx^T$ is a $3\times 3$ matrix
• C. $xx^T$ is a $1\times 1$ matrix
• D. $xx^T=x^Tx$

Answer 1

x is 1*3 Matrix

x^t is 3*1 matrix

x*x^t=order(1*1)

x^t*x=order(3*3)

hence (A) and (C) are answers

Answer 2

The matrix multiplication of a square/non-square matrix depends upon the order of the matrix.

Let $A_{m*n}$ and $B_{n*p}$ are two matrix then the order of resultant $[AB]_{m*p}$

now,

$x_{1*3}=\begin{bmatrix}3&1&2 \end{bmatrix}$

$x^T_{3*1}=\begin{bmatrix} 3\\ 1 \\ 2 \end{bmatrix}$

1.  form option A, [$x^Tx]_{3*3}$ is true.
2. option B is false because size of $xx^T$ should be $1*1$
3. option C is true.
4. option D is false.

$\text{option A,C is correct.}$