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

  1. $x^Tx$ is a $3\times 3$ matrix
  2. $xx^T$ is a $3\times 3$ matrix
  3. $xx^T$ is a $1\times 1$ matrix
  4. $xx^T=x^Tx$
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2 Answers

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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
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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.

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

 

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