# Matrices and Determinants · Mathematics · AP EAPCET

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AP EAPCET 2022 - 4th July Morning Shift
For $$i=1,2,3$$ and $$j=1,23$$ If $$a_i^2+b_i^2+c_i^2=1, a_i a_j+b_i b_j+c_i c_j=0, \forall i \neq j$$ and $$A=\left[\begin{array}{lll}a_1 & a_2 & a_3... AP EAPCET 2022 - 4th July Morning Shift If$$A=\frac{1}{7}\left[\begin{array}{ccc}3 & -2 & 6 \\ -6 & -3 & 2 \\ -2 & 6 & 3\end{array}\right]$$, then AP EAPCET 2022 - 4th July Morning Shift If$$A=\left[\begin{array}{cc}\alpha^2 & 5 \\ 5 & -\alpha\end{array}\right]$$and$$\operatorname{det}\left(A^{10}\right)=1024$$, then$$\alpha=$$... AP EAPCET 2022 - 4th July Morning Shift Let$$A=\left[\begin{array}{ccc}5 & \sin ^2 \theta & \cos ^2 \theta \\ -\sin ^2 \theta & -5 & 1 \\ \cos ^2 \theta & 1 & 5\end{array}\right]$$. Then, m... AP EAPCET 2022 - 4th July Morning Shift If$$\frac{x^4+24 x^2+28}{\left(x^2+1\right)^3}=\frac{A x+B}{x^2+1}+\frac{C x+D}{\left(x^2+1\right)^2}+\frac{E x+F}{\left(x^2+1\right)^3},$$then... AP EAPCET 2021 - 20th August Morning Shift The trace of the matrix$$A=\left[\begin{array}{ccc}1 & -5 & 7 \\ 0 & 7 & 9 \\ 11 & 8 & 9\end{array}\right]$$is AP EAPCET 2021 - 20th August Morning Shift If$$A, B$$and$$C$$are the angles of a triangle, then the system of equations$$-x+y \cos C+z \cos B=0, x \cos C-y+z \cos A=0$$and$$x \cos B+y \c...
AP EAPCET 2021 - 20th August Morning Shift
If $$\left[\begin{array}{cc}1 & -\tan \theta \\ \tan \theta & 1\end{array}\right]\left[\begin{array}{cc}1 & \tan \theta \\ -\tan \theta & 1\end{array}... AP EAPCET 2021 - 20th August Morning Shift What is the value of$$\left|\begin{array}{ccc}a & b & c \\ a-b & b-c & c-a \\ b+c & c+a & a+b\end{array}\right|$$? AP EAPCET 2021 - 19th August Evening Shift The value of$$\left|\begin{array}{ccc}b+c & a & a \\ b & c+a & b \\ c & c & a+b\end{array}\right|$$is AP EAPCET 2021 - 19th August Evening Shift Let$$A, B, C, D$$be square real matrices such that$$C^T=D A B, D^{\mathrm{T}}=A B C$$and$$S=A B C D$$, then$$S^2$$is equal to AP EAPCET 2021 - 19th August Evening Shift$$A=\left[\begin{array}{ccc}a^2 & 15 & 31 \\ 12 & b^2 & 41 \\ 35 & 61 & c^2\end{array}\right]$$and$$B=\left[\begin{array}{ccc}2 a & 3 & 5 \\ 2 & 2 b...
AP EAPCET 2021 - 19th August Evening Shift
Let $$a, b$$ and $$c$$ be such that $$b+c \neq 0$$ and \begin{aligned} & \left|\begin{array}{ccc} a & a+1 & a-1 \\ -b & b+1 & b-1 \\ c & c-1 & c+1 \... AP EAPCET 2021 - 19th August Morning Shift The equation whose roots are the values of the equation\left| {\matrix{ 1 & { - 3} & 1 \cr 1 & 6 & 4 \cr 1 & {3x} & {{x^2}} \cr } ...
AP EAPCET 2021 - 19th August Morning Shift
Let a and b be non-zero real numbers such that $$ab=5/2$$ and given $$A = \left[ {\matrix{ a & { - b} \cr b & a \cr } } \right]$$ and $$A{... AP EAPCET 2021 - 19th August Morning Shift If$$A=\left[\begin{array}{ccc}1 & -1 & 1 \\ 2 & 1 & -3 \\ 1 & 1 & 1\end{array}\right], 10 B=\left[\begin{array}{ccc}4 & 2 & 2 \\ -5 & 0 & \alpha \\ 1...
AP EAPCET 2021 - 19th August Morning Shift
The rank of the matrix $$\left[\begin{array}{ccc}4 & 2 & (1-x) \\ 5 & k & 1 \\ 6 & 3 & (1+x)\end{array}\right]$$ is 1 , then,
AP EAPCET 2021 - 19th August Morning Shift
If $$a_1, a_2, \ldots . a_9$$ are in GP, then $$\left|\begin{array}{lll}\log a_1 & \log a_2 & \log a_3 \\ \log a_4 & \log a_5 & \log a_6 \\ \log a_7 &... AP EAPCET 2021 - 19th August Morning Shift If$$\mathbf{a}=2 \hat{\mathbf{i}}+\hat{\mathbf{j}}+3 \hat{\mathbf{k}}, \mathbf{b}=\hat{\mathbf{i}}+3 \hat{\mathbf{j}}-\hat{\mathbf{k}}$$and$$\mathb...
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