One root of the equation - 3x-8 3 3 3 3x-8 3 3 3 3x-8 - is which of the following-

The correct option is B 2 / 3 3x 8 amp; 3 amp; 3 3 amp; 3x 8 amp; 3 3 amp; 3 amp; 3x 8 R _ 1 → R _ 1 R _ 2 ...

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Byju's Answer

Standard XII

Mathematics

Scalar Multiplication of a Matrix

One root of t...

Question

One root of the equation $∣ ∣ ∣ ∣ \begin{matrix} 3 x - 8 33 \end{matrix} \begin{matrix} 3 3 x - 8 3 \end{matrix} \begin{matrix} 33 3 x - 8 \end{matrix} ∣ ∣ ∣ ∣$ is which of the following?

\frac{8}{3}

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\frac{2}{3}

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\frac{1}{3}

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\frac{16}{3}

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Solution

The correct option is B $\frac{2}{3}$
$∣ ∣ ∣ ∣ \begin{matrix} 3 x - 8 & 3 & 3 3 & 3 x - 8 & 3 3 & 3 & 3 x - 8 \end{matrix} ∣ ∣ ∣ ∣$
$R_{1} \to R_{1} - R_{2}$
$∣ ∣ ∣ ∣ \begin{matrix} 3 x - 5 & - (3 x - 5) & 0 3 & 3 x - 8 & 3 3 & 3 & 3 x - 8 \end{matrix} ∣ ∣ ∣ ∣$
$R_{2} \to R_{2} - R_{3}$
$(3 x - 5) ∣ ∣ ∣ ∣ \begin{matrix} 1 & - 1 & 0 0 & 3 x - 5 & - (3 x - 5) 3 & 3 & 3 x - 8 \end{matrix} ∣ ∣ ∣ ∣ = 0$
${(3 x - 5)}^{2} ∣ ∣ ∣ ∣ \begin{matrix} 1 & - 1 & 0 0 & 1 & - 1 3 & 3 & 3 x - 8 \end{matrix} ∣ ∣ ∣ ∣ = 0$
${(3 x - 5)}^{2} (3 x - 5 + 3) = 0 \Rightarrow x = \frac{5}{3}, \frac{5}{3}, \frac{2}{3}$
Option B

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Q. If x<1 and

∣ ∣ ∣ ∣ \begin{matrix} 3 x - 8 & 3 & 3 3 & 3 x - 8 & 3 3 & 3 & 3 x - 8 \end{matrix} ∣ ∣ ∣ ∣

=0 then x=......

Q. Solve the following determinant equations:

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|\begin{matrix} x + a & b & c \\ a & x + b & c \\ a & b & x + c \end{matrix}| = 0

(ii)

|\begin{matrix} x + a & x & x \\ x & x + a & x \\ x & x & x + a \end{matrix}| = 0, a \neq 0

(iii)

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(iv)

|\begin{matrix} 1 & x & x^{2} \\ 1 & a & a^{2} \\ 1 & b & b^{2} \end{matrix}| = 0, a \neq b

(v)

|\begin{matrix} x + 1 & 3 & 5 \\ 2 & x + 2 & 5 \\ 2 & 3 & x + 4 \end{matrix}| = 0

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|\begin{matrix} 1 & x & x^{3} \\ 1 & b & b^{3} \\ 1 & c & c^{3} \end{matrix}| = 0, b \neq c

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|\begin{matrix} 15 - 2 x & 11 - 3 x & 7 - x \\ 11 & 17 & 14 \\ 10 & 16 & 13 \end{matrix}| = 0

(viii)

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(ix)

|\begin{matrix} 3 & - 2 & \sin (3 θ) \\ - 7 & 8 & \cos (2 θ) \\ - 11 & 14 & 2 \end{matrix}| = 0

Q. Solve the following determinant equations:

(i)

|\begin{matrix} x + a & b & c \\ a & x + b & c \\ a & b & x + c \end{matrix}| = 0

(ii)

|\begin{matrix} x + a & x & x \\ x & x + a & x \\ x & x & x + a \end{matrix}| = 0, a \neq 0

(iii)

|\begin{matrix} 3 x - 8 & 3 & 3 \\ 3 & 3 x - 8 & 3 \\ 3 & 3 & 3 x - 8 \end{matrix}| = 0

(iv)

|\begin{matrix} 1 & x & x^{2} \\ 1 & a & a^{2} \\ 1 & b & b^{2} \end{matrix}| = 0, a \neq b

(v)

|\begin{matrix} x + 1 & 3 & 5 \\ 2 & x + 2 & 5 \\ 2 & 3 & x + 4 \end{matrix}| = 0

(vi)

|\begin{matrix} 1 & x & x^{3} \\ 1 & b & b^{3} \\ 1 & c & c^{3} \end{matrix}| = 0, b \neq c

(vii)

|\begin{matrix} 15 - 2 x & 11 - 3 x & 7 - x \\ 11 & 17 & 14 \\ 10 & 16 & 13 \end{matrix}| = 0

(viii)

|\begin{matrix} 1 & 1 & x \\ p + 1 & p + 1 & p + x \\ 3 & x + 1 & x + 2 \end{matrix}| = 0

Q. Solve the following determinant equations:

(i)

|\begin{matrix} x + a & b & c \\ a & x + b & c \\ a & b & x + c \end{matrix}| = 0

(ii)

|\begin{matrix} x + a & x & x \\ x & x + a & x \\ x & x & x + a \end{matrix}| = 0, a \neq 0

(iii)

|\begin{matrix} 3 x - 8 & 3 & 3 \\ 3 & 3 x - 8 & 3 \\ 3 & 3 & 3 x - 8 \end{matrix}| = 0

(iv)

|\begin{matrix} 1 & x & x^{2} \\ 1 & a & a^{2} \\ 1 & b & b^{2} \end{matrix}| = 0, a \neq b

(v)

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(vii)

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Find the roots of the following equation applying quadratic formula.
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One root of the equation ∣∣ ∣∣3x−83333x−83333x−8∣∣ ∣∣ is which of the following?

One root of the equation $∣ ∣ ∣ ∣ \begin{matrix} 3 x - 8 33 \end{matrix} \begin{matrix} 3 3 x - 8 3 \end{matrix} \begin{matrix} 33 3 x - 8 \end{matrix} ∣ ∣ ∣ ∣$ is which of the following?