Let p be an odd prime number and Tp be the following set of 2 - 2 matrices TP- A- a b- c a - a- b- c - 0-1-2 - p-1

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Standard XII

Mathematics

Matrix Definition and Representation

Let p be an o...

Question

Let $p$ be an odd prime number and $T_{p}$ be the following set of $2 \times 2$ matrices $T_{P} = {A = [\begin{matrix} a & b c & a \end{matrix}] : a, b, c \in {0, 1, 2 . . . . p - 1}}$

Option a

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Option d

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Option b

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Option c

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Solution

The correct option is A Option a
Missing solution

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Let

p

be an odd prime number and

T_{p}

be the following set of

2 \times 2

matrices:

T_{p} = {A = [\begin{matrix} a & b c & a \end{matrix}] : a, b, c \in {0, 1, \dots ., p - 1}}

The number of A in

T_{p}

such that det(A) is not divisible by p is

Q. Let

A, B a n d C

2 \times 2

matrices with entries from the set of real numbers. Define

*

as follows:

A * B = \frac{1}{2} (A B + B A)

, then

Q. Let

P

be a point inside a triangle

A B C

with

∠ A B C = 90^{\circ}

. Let

P_{1}

and

P_{2}

be the images of

P

under reflection in

A B

and

B C

respectively. The distance between the circumcenters of triangles

A B C

and

P_{1} P P_{2}

Q. Let PQRST be a pentagon in which the sides PQ and RS are parallel and sides TP and QR are parallel. If PQ : RS is 3 : 1 and TP : QR is 1 : 2 and diagonals PS and QT meet at M, then PM : MS equals

A B C

is a right triangle right angled at

C .

Let

B C = a, C A = b, A B = c

and let

p

be the length of perpendicular from

C

A B

prove that

p c = a b

ii)

\frac{1}{p^{2}} = \frac{1}{a^{2}} + \frac{1}{b^{2}}

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Let p be an odd prime number and Tp be the following set of 2×2 matrices TP={A=[abca]:a,b,c∈{0,1,2....p−1}}

The correct option is A Option aMissing solution

Let $p$ be an odd prime number and $T_{p}$ be the following set of $2 \times 2$ matrices $T_{P} = {A = [\begin{matrix} a & b c & a \end{matrix}] : a, b, c \in {0, 1, 2 . . . . p - 1}}$

The correct option is A Option a
Missing solution