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Differentiabilty

Let A=[ x 2...

Question

Let $A = ⎛ ⎜ ⎝ \begin{matrix} x^{2} & 6 & 8 3 & y^{2} & 9 4 & 5 & z^{2} \end{matrix} ⎞ ⎟ ⎠$ and $B = ⎛ ⎜ ⎝ \begin{matrix} 2 x & 3 & 5 2 & 2 y & 6 1 & 4 & 2 z - 3 \end{matrix} ⎞ ⎟ ⎠$ be two matrices and if $T r (A) = T r (B)$ , then the value of $(x + y + z)$ is equal to
(Note: $T r (P)$ denotes trace of matrix $P$ )

A

0

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B

1

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C

2

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D

3

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Solution

The correct option is C $3$
$t r (A) = x^{2} + y^{2} + z^{2}$
$t r (B) = 2 x + 2 y + 2 z - 3$
$x^{2} + y^{2} + z^{2} = 2 x + 2 y + 2 z - 3$
${(x - 1)}^{2} + {(y - 1)}^{2} + (z - 1)^{2} = 0$
$x = y = z = 1$
Hence, $(x + y + z) = 3$

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Similar questions

A = d i a g (x^{2}, 6 x, 1)

B = d i a g (\frac{1}{x^{2}}, \frac{1}{x}, 1)

be two diagonal matrices. A function

f

f (x) = t r ((A^{- 1} B)^{- 1}) .

\int \frac{f (x)}{x^{2} + 1} d x = g (x)

g (0) = 0,

then the number of roots of

g (x) = 0

[t r (P)

denotes the trace of matrix

P]

x > 0,

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

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.
Two other matrices

X

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

Y = lim n \to \infty X

t r (P)

denotes the trace of matrix

P

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t r (A Y)

λ = 3,

\frac{1}{7} (t r (A B) + t r (B A))

t r (A)

denotes sum of diagonal elements of matrix

A

.

Q. If two square matrices

A

B

are of same order and,

T r (A) = 3, T r (B) = 5

T r (A + B) =

Q. Consider three matrices

A = [\begin{matrix} 2 & 1 4 & 1 \end{matrix}] B = [\begin{matrix} 3 & 4 2 & 3 \end{matrix}]

C = [\begin{matrix} 3 & - 4 - 2 & 3 \end{matrix}]

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The value of the sum

t r (A) + t r (\frac{A B C}{2}) + t r (\frac{A ({B C)}^{2}}{4}) + t r (\frac{A ({B C)}^{3}}{8}) + . . . . . . . . . . . . . + \infty

t r (A)

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