There are two values of -a- which makes determinant - 1 -2 5 2 a -1 0 4 2a -86- then find the sum of these numers-

| 1 amp; 2 amp; 5 2 #10; amp; a amp; 1 0 amp; 4 amp; 2a | =86 #10; #10; #160; #10; #10;Applying R_1R_1 2R ...

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Byju's Answer

Standard XII

Mathematics

Definition of a Determinant

There are two...

Question

There are two values of $^{'} a^{'}$ which makes determinant $Δ = ∣ ∣ ∣ ∣ \begin{matrix} 1 & - 2 & 5 2 & a & - 1 0 & 4 & 2 a \end{matrix} ∣ ∣ ∣ ∣ = 86$ , then find the sum of these numers.

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Solution

$∣ ∣ ∣ ∣ \begin{matrix} 1 & - 2 & 5 2 & a & - 1 0 & 4 & 2 a \end{matrix} ∣ ∣ ∣ ∣ = 86$

Applying $R_{1} \to R_{1} - 2 R_{2}$

$∣ ∣ ∣ ∣ \begin{matrix} 1 & - 2 & 5 0 & a + 4 & - 11 0 & 4 & 2 a \end{matrix} ∣ ∣ ∣ ∣ = 86$

$∣ ∣ ∣ \begin{matrix} a + 4 & - 11 4 & 2 a \end{matrix} ∣ ∣ ∣ = 86$

$(a - 4) 2 a - 44 = 86$

$2 a^{2} - 8 a - 42 = 86$

$a^{2} - 4 a - 21 = 86$

$(a + 3) (a - 7) = 86$

$(a + 3) = 86$

$a = 83$

$(a - 7) = 86$

$a = 91$

Hence, this is the answer.

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Similar questions

Q. There are two values of a which makes the determinant

∆ = |\begin{matrix} 1 & - 2 & 5 \\ 2 & a & - 1 \\ 0 & 4 & 2 a \end{matrix}|

equal to 86. The sum of these two values is

(a) 4
(b) 5
(c) −4
(d) 9

If there are two values of a which makes determinant, $Δ = ∣ ∣ ∣ ∣ \begin{matrix} 1 & - 2 & 5 2 & a & - 1 0 & 4 & 2 a \end{matrix} ∣ ∣ ∣ ∣ = 86$ , then the sum of these numbers is

(a) 4
(b) 5
(c) - 4
(d) 9

Q. There are two numbers x making the value of the determinant

∣ ∣ ∣ ∣ \begin{matrix} 1 & - 2 & 5 2 & x & - 1 0 & 4 & 2 x \end{matrix} ∣ ∣ ∣ ∣

equal to

86

. The sum of these two numbers, is?

Q. If

u_{n} = \int_{0}^{π / 2} \frac{1 - c o s 2 n x}{1 - c o s 2 x} d x

, then find the value of the determinant

Δ = ∣ ∣ ∣ ∣ \begin{matrix} u_{1} & u_{2} & u_{3} u_{4} & u_{5} & u_{6} u_{7} & u_{8} & u_{9} \end{matrix} ∣ ∣ ∣ ∣

Q. Which of these are correct?

(a)

If any two rows or columns of a determinant are identical, then the value of the determinant is zero.

(b)

If the corresponding rows and columns of a determinant are interchanged, then the value of the determinant does not change.

(c)

If any two rows (or column) of a determinant are interchanged, then the value of the determinant changes in sign.

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There are two values of ′a′ which makes determinant Δ=∣∣ ∣∣1−252a−1042a∣∣ ∣∣=86, then find the sum of these numers.

∣∣ ∣∣1−252a−1042a∣∣ ∣∣=86 Applying R1→R1−2R2 ∣∣ ∣∣1−250a+4−11042a∣∣ ∣∣=86 ∣∣∣a+4−1142a∣∣∣=86 (a−4)2a−44=86 2a2−8a−42=86 a2−4a−21=86 (a+3)(a−7)=86 (a+3)=86 a=83 (a−7)=86 a=91 Hence, this is the answer.

There are two values of $^{'} a^{'}$ which makes determinant $Δ = ∣ ∣ ∣ ∣ \begin{matrix} 1 & - 2 & 5 2 & a & - 1 0 & 4 & 2 a \end{matrix} ∣ ∣ ∣ ∣ = 86$ , then find the sum of these numers.