Recent questions 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

asked Nov 12, 2024 in Matrices & determinants by anil6198 (90 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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asked Jun 30, 2024 in Matrices & determinants by Shahidurrahman (565 points)

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asked Jun 16, 2024 in Matrices & determinants by Blahhhh (30 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.

asked Jun 13, 2024 in Matrices & determinants by sangna4378 (110 points)

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determinats and matrices

asked Jun 3, 2024 in Matrices & determinants by A.J. (15 points)

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1 answer

find the value of determinant

asked Apr 18, 2024 in Matrices & determinants by KritikaC (35 points)

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1 answer

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

asked Apr 8, 2024 in Matrices & determinants by Jiten Deshani (15 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)

+3 votes

2 answers

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

asked Feb 18, 2024 in Matrices & determinants by devendra8752 (25 points)

+19 votes

0 answers

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

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

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

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1 answer

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

asked Feb 7, 2024 in Matrices & determinants by tejas2856 (15 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

asked Dec 24, 2023 in Matrices & determinants by Georgian4911 (565 points)

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Let \( x =\left[\begin{array}{l}1 \\ 1 \\ 1\end{array}\right] \) and \( A=\left[\begin{array}{ccc}-1 & 2 & 3 \\ 0 & 1 & 6 \\ 0 & 0 & -1\end{array}\right] \). For \( k \in N \), if \( X^{\prime} A^{k} X=33 \), then \( k \) is equal to:

asked Dec 24, 2023 in Matrices & determinants by Georgian4911 (565 points)

+1 vote

1 answer

Let the matrix \( A=\left[\begin{array}{lll}0 & 1 & 0 \\ 0 & 0 & 1 \\ 1 & 0 & 0\end{array}\right] \) and the matrix \( B_{0}=A^{49}+2 A^{98} \). If \( B_{n}=\operatorname{Adj}\left(B_{n-1}\right) \) for all \( n \geq 1 \) then \( \operatorname{det}\left( B _{4}\right) \) is equal to : (1) \( 3^{28} \) (2) \( 3^{30} \) (3) \( 3^{32} \) (4) \( 3^{36} \)

asked Dec 24, 2023 in Matrices & determinants by Georgian4911 (565 points)

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Let \( A=\left(\begin{array}{cc}2 & -1 \\ 0 & 2\end{array}\right) \). If \( B=I-{ }^{5} C_{1}(\operatorname{adj} A)+{ }^{5} C_{2} \) \( (\operatorname{adj} A)^{2}-\ldots-{ }^{5} C_{5}(\operatorname{adj} A)^{5} \), then the sum of all elements of the matrix B is:

asked Dec 24, 2023 in Matrices & determinants by Georgian4911 (565 points)

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Let \( S=\{\sqrt{n}: 1 \leq n \leq 50 \) and \( n \) is odd \( \} \) Let \( a \in S \) and \( A=\left[\begin{array}{ccc}1 & 0 & a \\ -1 & 1 & 0 \\ -a & 0 & 1\end{array}\right] \) If \( \sum \operatorname{det}(\operatorname{adj} A)=100 \lambda \), then \( \lambda \) is equal to

asked Dec 24, 2023 in Matrices & determinants by Georgian4911 (565 points)

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If the system of linear equations \( 2 x-3 y=\gamma+5, \alpha x+5 y=\beta+1 \), where \( \alpha, \beta, \gamma \in R \) has infinitely many solutions, then the value of \( |9 \alpha+3 \beta+5 \gamma| \) is equal to

asked Dec 23, 2023 in Matrices & determinants by Georgian4911 (565 points)

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