Classify the following matrices as a row, a column, a square, a d… - Vidyadip

Question

Classify the following matrices as a row, a column, a square, a diagonal, a scalar, a unit, an upper triangular, a lower triangular, a symmetric or a skew- symmetric matrix :

$\left[\begin{array}{ccc}10 & -15 & 27 \\ -15 & 0 & \sqrt{34} \\ 27 & \sqrt{34} & \frac{5}{3}\end{array}\right]$

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Answer

Let $A=\left[\begin{array}{ccc}10 & -15 & 27 \\ -15 & 0 & \sqrt{34} \\ 27 & \sqrt{34} & \frac{5}{3}\end{array}\right]$

$\therefore \quad A^T=\left[\begin{array}{ccc}10 & -15 & 27 \\ -15 & 0 & \sqrt{34} \\ 27 & \sqrt{34} & \frac{5}{3}\end{array}\right]$

$\therefore A^{\top}=A, i / e_1, A=A^{\top}$

∴ A is a symmetric matrix.

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