The value of - 103 115 114- 111 108 106- 104 113 116 - 113 116 104- 108 106 111- 115 114 103 - is

Name: JEE- Grade 12- Mathematics- Matrices and Determinants- Session 06- D10
Uploaded: 2022-07-04T10:36:42+05:30
Description: Let, D_1=|[ 103 amp; 115 amp; 114; 111 amp; 108 amp; 106; 104 amp; 113 amp; 116 ]|,D_2=|[ 113 amp; 116 amp; 104; 108 amp; 106 amp; 111; ...

Let, D_1=|[ 103 amp; 115 amp; 114; 111 amp; 108 amp; 106; 104 amp; 113 amp; 116 ]|,D_2=|[ 113 amp; 116 amp; 104; 108 amp; 106 amp; 111; ...

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Standard VI

Mathematics

HCF

The value of ...

Question

The value of $∣ ∣ ∣ ∣ \begin{matrix} 103 & 115 & 114 111 & 108 & 106 104 & 113 & 116 \end{matrix} ∣ ∣ ∣ ∣ + ∣ ∣ ∣ ∣ \begin{matrix} 113 & 116 & 104 108 & 106 & 111 115 & 114 & 103 \end{matrix} ∣ ∣ ∣ ∣$ is

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Solution

Let, $D_{1} = ∣ ∣ ∣ ∣ \begin{matrix} 103 & 115 & 114 111 & 108 & 106 104 & 113 & 116 \end{matrix} ∣ ∣ ∣ ∣, D_{2} = ∣ ∣ ∣ ∣ \begin{matrix} 113 & 116 & 104 108 & 106 & 111 115 & 114 & 103 \end{matrix} ∣ ∣ ∣ ∣ D = ∣ ∣ ∣ ∣ \begin{matrix} 103 & 115 & 114 111 & 108 & 106 104 & 113 & 116 \end{matrix} ∣ ∣ ∣ ∣ + ∣ ∣ ∣ ∣ \begin{matrix} 113 & 116 & 104 108 & 106 & 111 115 & 114 & 103 \end{matrix} ∣ ∣ ∣ ∣$
In $D_{2}$ , interchanging $C_{1}$ and $C_{3}$
$D = ∣ ∣ ∣ ∣ \begin{matrix} 103 & 115 & 114 111 & 108 & 106 104 & 113 & 116 \end{matrix} ∣ ∣ ∣ ∣ - ∣ ∣ ∣ ∣ \begin{matrix} 104 & 116 & 113 111 & 106 & 108 103 & 114 & 115 \end{matrix} ∣ ∣ ∣ ∣$
In $D_{2}$ , interchanging $C_{2}$ and $C_{3}$
$D = ∣ ∣ ∣ ∣ \begin{matrix} 103 & 115 & 114 111 & 108 & 106 104 & 113 & 116 \end{matrix} ∣ ∣ ∣ ∣ + ∣ ∣ ∣ ∣ \begin{matrix} 104 & 113 & 116 111 & 108 & 106 103 & 115 & 114 \end{matrix} ∣ ∣ ∣ ∣$
In $D_{2}$ , interchanging $R_{1}$ and $R_{3}$
$D = ∣ ∣ ∣ ∣ \begin{matrix} 103 & 115 & 114 111 & 108 & 106 104 & 113 & 116 \end{matrix} ∣ ∣ ∣ ∣ - ∣ ∣ ∣ ∣ \begin{matrix} 103 & 115 & 114 111 & 108 & 106 104 & 113 & 116 \end{matrix} ∣ ∣ ∣ ∣ = 0$

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Similar questions

Q. The value of sum of the given determinants,

| A | = ∣ ∣ ∣ ∣ \begin{matrix} 103 & 115 & 114 111 & 108 & 106 104 & 113 & 116 \end{matrix} ∣ ∣ ∣ ∣, | B | = ∣ ∣ ∣ ∣ \begin{matrix} 113 & 116 & 104 108 & 106 & 111 115 & 114 & 103 \end{matrix} ∣ ∣ ∣ ∣

Complete the table below:

$\begin{matrix} O u t p u t (U n i t s) & A v e r a g e C o s t (R s .) & M a r g i n a l C o s t (R s .) 1 & 12 & - 2 & 10 & - 3 & - & 10 4 & 10.5 & - 5 & 11 & - 6 & - & 17 \end{matrix}$

97, 101, 103, 107, 111, 113

Q. Let

A_{1} = [a_{1}] A_{2} = [\begin{matrix} a_{2} & a_{3} a_{4} & a_{5} \end{matrix}] A_{3} = ⎡ ⎢ ⎣ \begin{matrix} a_{6} & a_{7} & a_{8} a_{9} & a_{10} & a_{11} a_{12} & a_{13} & a_{14} \end{matrix} ⎤ ⎥ ⎦ \dots \dots A_{n} = [\dots] where a_{r} = [{log}_{2} r]

([\cdot]

denotes the greatest integer

)

. Then trace of

A_{10}

Tick the correct answer:- In a homogeneous solution, the dimension of solute particles varies between:
a. 1 – 103 nm b. 104 - 106 nm
c. 105 - 106 nm d. 108 – 109 nm

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The value of ∣∣ ∣∣103115114111108106104113116∣∣ ∣∣+∣∣ ∣∣113116104108106111115114103∣∣ ∣∣ is

The value of $∣ ∣ ∣ ∣ \begin{matrix} 103 & 115 & 114 111 & 108 & 106 104 & 113 & 116 \end{matrix} ∣ ∣ ∣ ∣ + ∣ ∣ ∣ ∣ \begin{matrix} 113 & 116 & 104 108 & 106 & 111 115 & 114 & 103 \end{matrix} ∣ ∣ ∣ ∣$ is