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Question

Give an example of a square matrix which is not diagonal.

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Solution

$A s q u a r e m a t r i x w h o s e a l l e l e m e n t s e x c e p t t h e d i a g o n a l e l e m e n t s a r e z e r o i s c a l l e d a d i a g o n a l m a t r i x . A m a t r i x w h i c h i s n o t d i a g o n a l = [\begin{matrix} 3 & 7 & 8 \\ 0 & 2 & 0 \\ 1 & 0 & 5 \end{matrix}]$

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Q. Given an example of
(i) a row matrix which is also a column matrix,
(ii) a diagonal matrix which is not scalar,
(iii) a triangular matrix

Q. Are the square roots of all positive integers irrational? If not, give an example of the square of a number which is rational number.

Q. _____ matrix is a square matrix in which all the elements other than the principal diagonal elements are zero.

A = [\begin{matrix} 0 & 0 & 4 \\ 0 & 4 & 0 \\ 4 & 0 & 0 \end{matrix}]

is a

(a) square matrix
(b) diagonal matrix
(c) unit matrix
(d) none of these

Q. Assertion :The matrix

⎡ ⎢ ⎣ \begin{matrix} a & 0 & 0 & 0 0 & b & 0 & 0 0 & 0 & c & 0 \end{matrix} ⎤ ⎥ ⎦

is a diagonal matrix Reason:

A [a_{i j}]

is a square matrix such that

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i \neq j

A

is called diagonal matrix.

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