Recent questions and answers in Matrices & determinants

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15. If for the matrix, \( A=\left[\begin{array}{cc}1 & -\alpha \\ \alpha & \beta\end{array}\right], A A^{T}=I_{2} \), then the value of \( \alpha^{4}+\beta^{4} \) is : (1) 4 (2) 2 (3) 3 (4) 1

answered Nov 13, 2024 in Matrices & determinants by PrachiKumari (30.8k points)

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\( 0.9 \quad \) If \( \Delta_{r}=\left|\begin{array}{ccc}r & n & 6 \\ r^{2} & 2 n^{2} & 4 n-2 \\ r^{3} & 3 n^{3} & 3 n^{2}-3 n\end{array}\right| \), then \( \sum_{r=0}^{n-1} \Delta_{r} \) equals to (1) \( n^{2}(n+2) \) (2) \( n(n+2)^{2} \) (3) \( \frac{1}{12} n\left(n^{3}+2\right) \) (4) none of these

answered Oct 1, 2024 in Matrices & determinants by khadarabad (1.5k points)

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\( \left|\begin{array}{ccc}x+1 & 2 & 3 \\ 2 & x+4 & 6 \\ 3 & 6 & x+9\end{array}\right| \) is decressing in.

answered Sep 13, 2024 in Matrices & determinants by khadarabad (1.5k points)

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You are given the network of bus routes between the bus terminals of three cities A, B and C.

asked Aug 27, 2024 in Matrices & determinants by asdfghjkl1 (250 points)

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In a school, there are two book stores. Store A sold 10 dozen Mathematics books,

asked Aug 27, 2024 in Matrices & determinants by asdfghjkl1 (250 points)

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If \( A=\left[\begin{array}{cc}\sqrt{2} & 1 \\ -1 & \sqrt{2}\end{array}\right], B=\left[\begin{array}{ll}1 & 0 \\ 1 & 1\end{array}\right], C=A B A^{T} \) and \( X=A^{\top} C^{2} A \), then \( \operatorname{det} X \) is equal to : (1) 243 (2) 891 (3) 729

answered Aug 13, 2024 in Matrices & determinants by khadarabad (1.5k points)

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answered Jul 1, 2024 in Matrices & determinants by SamikshaKumari (63.8k points)

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(a) Let \( A=\left[\begin{array}{ccc}\sqrt{2} & 1 & 0 \\ 1 & -\sqrt{2} & 0 \\ 0 & 0 & \sqrt{3}\end{array}\right] \), then the value of \( \frac{\left|A^{-1}+A^{T}\right|}{|\operatorname{adj} .(\operatorname{adj} . A)|} \) is equal to

answered Jun 20, 2024 in Matrices & determinants by khadarabad (1.5k points)

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answered Jun 17, 2024 in Matrices & determinants by AnjilJain (60.1k points)

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determinats and matrices

answered Jun 4, 2024 in Matrices & determinants by YashikaPatil (41.2k points)

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71. (a) Let \( A=\left[\begin{array}{ccc}\sqrt{2} & 1 & 0 \\ 1 & -\sqrt{2} & 0 \\ 0 & 0 & \sqrt{3}\end{array}\right] \), then the value of \( \frac{\left|A^{-1}+A^{T}\right|}{|\operatorname{adj} \cdot(\operatorname{adj} \cdot A)|} \) is equal to 1) \( -\frac{2^{6} \sqrt{3}}{3^{8}} \) 2) \( \frac{2^{3}}{3^{6} \sqrt{3}} \) 3) \( -\frac{2^{9} \sqrt{3}}{3^{6}} \) 4) \( \frac{2^{3}}{3^{5}} \)

answered May 29, 2024 in Matrices & determinants by khadarabad (1.5k points)

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find the value of determinant

answered May 3, 2024 in Matrices & determinants by khadarabad (1.5k points)

+1 vote

2 answers

Let the area of the triangle with vertices \( A (1, \alpha), B (\alpha, 0) \) and \( C (0, \alpha) \) be 4 sq. units. If the point \( (\alpha,-\alpha),(-\alpha, \alpha) \) and \( \left(\alpha^{2}, \beta\right) \) are collinear, then \( \beta \) is equal to

answered Apr 14, 2024 in Matrices & determinants by khadarabad (1.5k points)

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Let \( A =\left[\begin{array}{rrr}1 & -2 & \alpha \\ \alpha & 2 & -1\end{array}\right] \) and \( B =\left[\begin{array}{rr}2 & \alpha \\ -1 & 2 \\ 4 & -5\end{array}\right], \alpha \in C \). Then the absolute value of the sum of all values of \( \alpha \) for which \( \operatorname{det}(A B)=0 \) is : (A) 3 (B) 4 (C) 2 (D) 5

answered Apr 9, 2024 in Matrices & determinants by Bhagvad (50.3k points)

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Let a and b alpha belongs to c then the absolute value of the sum of all value of alpha for which detab=0

answered Apr 9, 2024 in Matrices & determinants by AnkushLather (50.1k points)

+17 votes

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To find matrix B and C

asked Feb 20, 2024 in Matrices & determinants by Ashu:6689 (25 points)

+1 vote

1 answer

If A=[2-3][3-2][-1 4],B=[-3 4 1][2-1-3] verify, [3A-5Bt]t=3At-5B

answered Feb 17, 2024 in Matrices & determinants by PritiJawadwar (48.9k points)

+19 votes

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Verify, 3A-5Bt =3At-5B

asked Feb 16, 2024 in Matrices & determinants by pranay8492 (35 points)

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If A = [[1, 0, 0], [5, 1, 0], [1, 3, 1]], find the matrix B such that AB = I. Verify that BA = I.

answered Feb 7, 2024 in Matrices & determinants by KalyaniMeshram (36.2k points)

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Consider a matrix \( A=\left[\begin{array}{ccc}\alpha & \beta & \gamma \\ \alpha^{2} & \beta^{2} & \gamma^{2} \\ \beta+\gamma & \gamma+\alpha & \alpha+\beta\end{array}\right] \), where \( \alpha, \beta, \gamma \) are three distinct natural numbers. If \( \frac{\operatorname{det}(\operatorname{adj}(\operatorname{adj}(\operatorname{adj}(\operatorname{adj} A))))}{(\alpha-\beta)^{16}(\beta-\gamma)^{16}(\gamma-\alpha)^{16}}=2^{32} \times 3^{16} \), then the number of such 3 - tuples \( (\alpha, \beta, \gamma) \) is

answered Dec 24, 2023 in Matrices & determinants by AsthaPatel (47.9k points)

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