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General

Easy

Question

Let A be a square matrix. Then which of the following is not a symmetric matrix -

A + $A^{'}$
A $A^{'}$
$A^{'}$ A
A – $A^{'}$

The correct answer is: A $straight A to the power of straight prime$

We are asked to find which of the given options is not a symmetric matrix
A is a square matrix (A - A')'
= A' - (A')'
=A' - A
hence it is not a symmetric matrix

Therefore we find that A -A' is not a symmetric matrix

If A is a square matrix, then A– $straight A to the power of straight prime$ is -

Maths-General

General

maths-

If A is symmetric matrix and B is a skew- symmetric matrix, then for n $element of$ N, false statement is -

maths-General

General

Maths-

If A – $straight A to the power of straight prime$ = 0, then $straight A to the power of straight prime$ is -

Maths-General

General

Maths-

If A is a matrix of order 3 × 4, then both AB^T and B^TA are defined if order of B is -

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General

maths-

If A = $open square brackets table row cell cos invisible function application alpha end cell cell sin invisible function application alpha end cell row cell negative sin invisible function application alpha end cell cell cos invisible function application alpha end cell end table close square brackets$ , then $A A to the power of straight prime$ equals -

maths-General

General

Maths-

Consider the cubic equation $x cubed minus left parenthesis 1 plus cos space theta plus sin space theta right parenthesis x squared plus left parenthesis cos space theta sin space theta plus cos space theta plus sin space theta right parenthesis x minus sin space theta cos space theta equals 0$ whose roots are x₁, x₂, and x₃
The value of $x subscript 1 superscript 2 plus x subscript 2 superscript 2 plus x subscript 3 superscript 2$ equals

In this question, we have to given the cubic equation and its root x1,x2,x3 and we have to find the
$x 1 squared plus x 2 squared plus x 3 squared$ .Use, $left parenthesis x 1 plus x 2 plus x 3 right parenthesis squared equals x 1 squared plus x 2 squared plus x 3 squared plus 2 left parenthesis x 1 x 2 plus x 2 x 3 plus x 3 x 1 right parenthesis$ and sum of roots is $fraction numerator negative c over denominator a end fraction$ and product of roots is b/a.

Consider the cubic equation $x cubed minus left parenthesis 1 plus cos space theta plus sin space theta right parenthesis x squared plus left parenthesis cos space theta sin space theta plus cos space theta plus sin space theta right parenthesis x minus sin space theta cos space theta equals 0$ whose roots are x₁, x₂, and x₃
The value of $x subscript 1 superscript 2 plus x subscript 2 superscript 2 plus x subscript 3 superscript 2$ equals

Maths-General

General

Maths-