Let A- 2 0 7- 0 1 0- 1 -2 1 - and - - 14- 7- 0 1 0- - -4- -2- - If AB-I- where I is an identity matrix of order 3 then trace B has value equal to

The correct option is A 0 x=0.47777 100 x=47.777 10 x=4.77790 x=43 x=4390 x=0.001 x=0.001001001 100 x=.100100100 10 ...

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Byju's Answer

Standard XII

Mathematics

Identity Matrix

Let A=[ 2 0...

Question

Let $A = ⎡ ⎢ ⎣ \begin{matrix} 2 & 0 & 7 0 & 1 & 0 1 & - 2 & 1 \end{matrix} ⎤ ⎥ ⎦$ and $⎡ ⎢ ⎣ \begin{matrix} - α & 14 α & 7 α 0 & 1 & 0 α & - 4 α & - 2 α \end{matrix} ⎤ ⎥ ⎦$ . If $A B = I$ , where $I$ is an identity matrix of order $3$ then trace $B$ has value equal to

0

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5

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Solution

The correct option is A $0$
$x = 0.47777$
$100 x = 47.777$
$\frac{10 x = 4.777}{90 x = 43}$
$x = \frac{43}{90}$

$x = 0.001$
$x = 0.001001001$
$100 x = .100100100$
$\frac{100000 x = 100.100100}{99900 x = 99}$
$x = \frac{99}{99900}$
$x = \frac{11}{11100}$

$A = ⎡ ⎢ ⎣ \begin{matrix} 2 & 0 & 7 0 & 1 & 0 1 & - 2 & 1 \end{matrix} ⎤ ⎥ ⎦$
$B = ⎡ ⎢ ⎣ \begin{matrix} - α & 14 α & 7 α 0 & 1 & 0 α & - 4 α & 2 α \end{matrix} ⎤ ⎥ ⎦$
$A B = ⎡ ⎢ ⎣ \begin{matrix} - 2 α + 0 - 7 α & 0 + 0 + 0 & 2 α + 0 - 2 α 0 + 0 + 0 & 0 + 1 + 0 & 8 α 0 & 0 & 9 α \end{matrix} ⎤ ⎥ ⎦$
$α = \frac{1}{9}$
trace $(B) = 0$

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Similar questions

Q. Let

P = ⎡ ⎢ ⎣ \begin{matrix} 323 \end{matrix} \begin{matrix} - 1 0 - 5 \end{matrix} \begin{matrix} - 2 α 0 \end{matrix} ⎤ ⎥ ⎦

, where

α \in R

. Suppose

Q = [q_{i j}]

is matrix such that

P Q = k I

, where

k \in R, k \neq 0

and

I

is the identity matrix of order

3

. If

q_{23} = - \frac{k}{8}

and

d e t (Q) = \frac{k^{2}}{2}

, then

Q. The value of x is such that matrix product

⎡ ⎢ ⎣ \begin{matrix} 2 & 0 & 7 0 & 1 & 0 1 & - 2 & 1 \end{matrix} ⎤ ⎥ ⎦ ⎡ ⎢ ⎣ \begin{matrix} - x & 14 x & 7 x 0 & 1 & 0 x & - 4 x & - 2 x \end{matrix} ⎤ ⎥ ⎦

equals an identity matrix. Then the value of 20x is

Q. Let

A = ⎡ ⎢ ⎣ \begin{matrix} 2 & 0 & 7 0 & 1 & 0 1 & - 2 & 1 \end{matrix} ⎤ ⎥ ⎦

and

B = ⎡ ⎢ ⎣ \begin{matrix} - x & 14 x & 7 x 0 & 1 & 0 x & - 4 x & - 2 x \end{matrix} ⎤ ⎥ ⎦

are two matrices such that

A B = (A B)^{- 1}

and

A B \neq I

(where

I

is an identity matrix of order

3 \times 3

).
Find the value of

T r . (A B + (A B)^{2} + (A B)^{3} + . . . + (A B)^{100})

where

T r . (A)

denotes the trace of matrix

A

Q. Let

P = ⎡ ⎢ ⎣ \begin{matrix} 3 & - 1 & - 2 2 & 0 & α 3 & - 5 & 0 \end{matrix} ⎤ ⎥ ⎦

, where

α \in R

. Suppose

Q = [q_{i j}]

is a matrix such that

P Q = k I

, where

k \in R, k \neq 0

and

I

the identity matrix of order

3

. If

q_{23} = - \frac{k}{8}

and

det (Q) = \frac{k^{2}}{2}

, then:

Q. For

x > 0,

let

A = ⎡ ⎢ ⎢ ⎢ ⎣ \begin{matrix} x + \frac{1}{x} & 0 & 0 0 & x & 0 0 & 0 & 16 \end{matrix} ⎤ ⎥ ⎥ ⎥ ⎦

and

B = ⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ \begin{matrix} \frac{5 x}{x^{2} + 1} & 0 & 0 0 & \frac{3}{x} & 0 0 & 0 & \frac{1}{4} \end{matrix} ⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦

be two matrices.
Three other matrices

X, Y

and

Z

are defined as

X = (A B)^{- 1} + (A B)^{- 2} + {A B}^{- 3} + \dots (A B)^{- n},

Y = lim n \to \infty X

and

Z = Y^{- 1} - 2 I,

where

I

is the identity matrix of order

3.

t r (P)

denotes the trace of matrix

P

and

a d j (P)

denotes the adjoint of matrix

P

, then which of the following is/are CORRECT?

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Let A=⎡⎢⎣2070101−21⎤⎥⎦ and ⎡⎢⎣−α14α7α010α−4α−2α⎤⎥⎦. If AB=I, where I is an identity matrix of order 3 then trace B has value equal to

Let $A = ⎡ ⎢ ⎣ \begin{matrix} 2 & 0 & 7 0 & 1 & 0 1 & - 2 & 1 \end{matrix} ⎤ ⎥ ⎦$ and $⎡ ⎢ ⎣ \begin{matrix} - α & 14 α & 7 α 0 & 1 & 0 α & - 4 α & - 2 α \end{matrix} ⎤ ⎥ ⎦$ . If $A B = I$ , where $I$ is an identity matrix of order $3$ then trace $B$ has value equal to