Have a query? Ask a Tutor!!

Access to best educators and exclusive paper discussions

Offsite Campus Turito Championship

Can’t find what you’re looking for?

Our tutors are from top schools around the world, and they are waiting for you 24/7, anytime, anywhere.

Homework- One to One Solutions
Understand concepts to solve better
Get your doubts solved instantly

Maths-

General

Easy

Question

If $A equals open square brackets table row 4 cell x plus 2 end cell row cell 2 x minus 3 end cell cell x plus 1 end cell end table close square brackets$ is symmetric then trace of A is

5
-10
10
15

hint Hint:

A square matrix B which of size n × n is considered to be symmetric if and only if B^T = B. Consider the given matrix B, that is, a square matrix that is equal to the transposed form of that matrix, called a symmetric matrix.
This can be represented as: If B = ${[b_{i j}]}_{n \times n}$ is the symmetric matrix, then $b_{i j}$ = $b_{j i}$ for all i and j or 1 ≤ i ≤ n, and 1 ≤ j ≤ n. Here,

n is any natural number.

$b_{i j}$ is an element at position (i, j) which is i^th row and j^thcolumn in matrix B and

$b_{j i}$ is an element at position (j, i) which is j^th row and i^th column in matrix B.

The correct answer is: 10

Given $A equals open square brackets table row 4 cell x plus 2 end cell row cell 2 x minus 3 end cell cell x plus 1 end cell end table close square brackets$ is symmetric.
$A to the power of T space equals space A T r a n s p o s e space i s space i n t e r c h a n g i n g space o f space r o w s space a n d space c o l u m n s space i n space a space m a t r i x. rightwards double arrow open square brackets table row 4 cell 2 x space minus space 3 end cell row cell x space plus space 2 end cell cell x space plus space 1 end cell end table close square brackets space equals space open square brackets table row 4 cell x space plus space 2 end cell row cell 2 x space minus space 3 end cell cell x space plus space 1 end cell end table close square brackets E q u a t i n g rightwards double arrow space x plus space 2 space equals space 2 x space minus space 3 rightwards double arrow x space space equals space 5 T h e r e f o r e space A space equals space open square brackets table row 4 cell 5 space plus space 2 end cell row cell 2 left parenthesis 5 right parenthesis space minus space 3 end cell cell 5 space plus space 1 end cell end table close square brackets space equals space open square brackets table row 4 7 row 7 6 end table close square brackets T r left parenthesis A right parenthesis space equals space I n space a space comma m a t r i x space s u m space o f space p r i n c i p a l space d i a g o n a l space e l e m e n t s space i s space c a l l e d space a s space t r a c e T r left parenthesis A right parenthesis space equals space 4 space plus space 6 space equals space 10$
Thus, trace of A is 10.

Related Questions to study

The oxidation number of Mn in the product of alkaline oxidative fusion of MnO₂ is

The oxidation number of Mn in the product of alkaline oxidative fusion of MnO₂ is

chemistry-General

When a satellite going round the earth in a circular orbit of radius r and speed v loses some of its energy, then r and v changes as

When a satellite going round the earth in a circular orbit of radius r and speed v loses some of its energy, then r and v changes as

If $f open parentheses x close parentheses equals vertical line log subscript 10 end subscript invisible function application x vertical line$ , then at $x equals 1$

If $f open parentheses x close parentheses equals vertical line log subscript 10 end subscript invisible function application x vertical line$ , then at $x equals 1$

parallel

If $open parentheses table row cell x minus 2 y end cell cell 5 y end cell row 6 cell a minus 2 b end cell end table close parentheses equals 5 open parentheses table attributes columnalign left end attributes row 4 2 row cell fraction numerator b over denominator 5 end fraction end cell 6 end table close parentheses$ then a + x =

If $open parentheses table row cell x minus 2 y end cell cell 5 y end cell row 6 cell a minus 2 b end cell end table close parentheses equals 5 open parentheses table attributes columnalign left end attributes row 4 2 row cell fraction numerator b over denominator 5 end fraction end cell 6 end table close parentheses$ then a + x =

Which of the following statements about the interstitial compounds is incorrect?

Which of the following statements about the interstitial compounds is incorrect?

chemistry-General

Potential energy of a satellite having mass m and rotating at a height of 6.4 $cross times 10 to the power of 6$ m from the surface of earth

Potential energy of a satellite having mass m and rotating at a height of 6.4 $cross times 10 to the power of 6$ m from the surface of earth

parallel

The slant height of a cone is fixed as 7 cm. If the rate of increase in its height is 0.3 cm/sec. Then the rate of increase in volume when the height is 4cm

The slant height of a cone is fixed as 7 cm. If the rate of increase in its height is 0.3 cm/sec. Then the rate of increase in volume when the height is 4cm

A satellite with K.E. E_K is revolving round the earth in a circular orbit. How much more K.E. should be given to it so that it may just escape into outer space?

A satellite with K.E. E_K is revolving round the earth in a circular orbit. How much more K.E. should be given to it so that it may just escape into outer space?

If A,B,C are the maximum velocities of the particles moving according to the law $S equals 60 t minus 5 t to the power of 3 end exponent comma S equals 6 t minus fraction numerator 1 over denominator 2 end fraction t to the power of 3 end exponent comma S equals 10 t minus 7 t to the power of 3 end exponent$ respectively then the ascending order of A,B,C is

If A,B,C are the maximum velocities of the particles moving according to the law $S equals 60 t minus 5 t to the power of 3 end exponent comma S equals 6 t minus fraction numerator 1 over denominator 2 end fraction t to the power of 3 end exponent comma S equals 10 t minus 7 t to the power of 3 end exponent$ respectively then the ascending order of A,B,C is

parallel

A satellite moves around the earth in a circular orbit of radius r with speed v, If mass of the satellite is M, its total energy is

A satellite moves around the earth in a circular orbit of radius r with speed v, If mass of the satellite is M, its total energy is

Which one of the following d-block elements has half-filled penultimate d-subshell as well as half filled penultimate d-subshell as well as half filled valence s-subshell?

Which one of the following d-block elements has half-filled penultimate d-subshell as well as half filled penultimate d-subshell as well as half filled valence s-subshell?

chemistry-General

A conical vessel of height 10ft and semivertical angle $30 to the power of ring operator end exponent$ is full of water. If empties in such away that the height at the water in the vessel is decreasing at a constant rate of 1ft/min. Then the rate at which the volume of water in the vessel is decreasing when its height is 6ft. is

A conical vessel of height 10ft and semivertical angle $30 to the power of ring operator end exponent$ is full of water. If empties in such away that the height at the water in the vessel is decreasing at a constant rate of 1ft/min. Then the rate at which the volume of water in the vessel is decreasing when its height is 6ft. is

parallel

If the gravitational force between two objects were proportional to $1 over R$ (and not as $1 over R squared$ )where R is separation between them, then a particle in circular orbit under such a force would have, its orbital speed v proportional to

If the gravitational force between two objects were proportional to $1 over R$ (and not as $1 over R squared$ )where R is separation between them, then a particle in circular orbit under such a force would have, its orbital speed v proportional to

The surface area of a sphere increases at the rate of 1 sq. ft per second, then the rate of increase of volume when the radius is $3 f t$ is

The surface area of a sphere increases at the rate of 1 sq. ft per second, then the rate of increase of volume when the radius is $3 f t$ is

If $f open parentheses x close parentheses equals open curly brackets table row cell fraction numerator x minus 1 over denominator 2 x to the power of 2 end exponent minus 7 x plus 5 end fraction comma blank f o r x not equal to 1 end cell row cell negative fraction numerator 1 over denominator 3 end fraction comma blank f o r x equals 1 end cell end table close$ , then $f to the power of ´ end exponent left parenthesis 1 right parenthesis$ is equal to

If $f open parentheses x close parentheses equals open curly brackets table row cell fraction numerator x minus 1 over denominator 2 x to the power of 2 end exponent minus 7 x plus 5 end fraction comma blank f o r x not equal to 1 end cell row cell negative fraction numerator 1 over denominator 3 end fraction comma blank f o r x equals 1 end cell end table close$ , then $f to the power of ´ end exponent left parenthesis 1 right parenthesis$ is equal to

parallel

card img

With Turito Academy.

card img

With Turito Foundation.

card img

Get an Expert Advice From Turito.

Turito Academy

card img

With Turito Academy.

Test Prep

card img

With Turito Foundation.