79457
If \(a, b, c\) are the integers between 1 and 9 and a51, b41, c31 are three digit numbers and the value of determinant \(D=\left|\begin{array}{ccc}5 & 4 & 3 \\ \text { a51 } & \text { b41 } & \text { c31 } \\ a & b & c\end{array}\right|\) is zero, then \(a, b, c\) are
79458
Let \(A=\left[\begin{array}{rrrr}1 & 0 & -1 & -3 \\ 0 & 1 & 1 & k-1 \\ 0 & 0 & k-1 & 1\end{array}\right]\) and \(k \in R\). Then the value of \(k\) if exists for which the rank of \(A\) is 2 , is
1 1
2 does not exist
3 \(1 / 3\)
4 \(1,1 / 3\)
Explanation:
(B) : Given, \(A=\left[\begin{array}{llll}1 & 0 & -1 & -3 \\ 0 & 1 & 1 & \mathrm{k}-1 \\ 0 & 0 & \mathrm{k}-1 & 1\end{array}\right]\) Applying \(\mathrm{R}_{2} \rightarrow \mathrm{R}_{2}+\mathrm{R}_{3}\) \(A=\left[\begin{array}{llll} 1 & 0 & -1 & -3 \\ 0 & 1 & \mathrm{k} & \mathrm{k} \\ 0 & 0 & \mathrm{k}-1 & 1 \end{array}\right]\) The value of \(k\) does not exis or the rank of 2 is not possible in this case
AP EAMCET-2022-06.07.2022
Matrix and Determinant
79459
A value of \(b\) for which the rank of the matrix \(A=\left[\begin{array}{cccc} 1 & 1 & -1 & 0 \\ 4 & 4 & -3 & 1 \\ b & 2 & 2 & 2 \\ 9 & 9 & b & 3 \end{array}\right] \text { is } 3 \text {, is }\)
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Matrix and Determinant
79457
If \(a, b, c\) are the integers between 1 and 9 and a51, b41, c31 are three digit numbers and the value of determinant \(D=\left|\begin{array}{ccc}5 & 4 & 3 \\ \text { a51 } & \text { b41 } & \text { c31 } \\ a & b & c\end{array}\right|\) is zero, then \(a, b, c\) are
79458
Let \(A=\left[\begin{array}{rrrr}1 & 0 & -1 & -3 \\ 0 & 1 & 1 & k-1 \\ 0 & 0 & k-1 & 1\end{array}\right]\) and \(k \in R\). Then the value of \(k\) if exists for which the rank of \(A\) is 2 , is
1 1
2 does not exist
3 \(1 / 3\)
4 \(1,1 / 3\)
Explanation:
(B) : Given, \(A=\left[\begin{array}{llll}1 & 0 & -1 & -3 \\ 0 & 1 & 1 & \mathrm{k}-1 \\ 0 & 0 & \mathrm{k}-1 & 1\end{array}\right]\) Applying \(\mathrm{R}_{2} \rightarrow \mathrm{R}_{2}+\mathrm{R}_{3}\) \(A=\left[\begin{array}{llll} 1 & 0 & -1 & -3 \\ 0 & 1 & \mathrm{k} & \mathrm{k} \\ 0 & 0 & \mathrm{k}-1 & 1 \end{array}\right]\) The value of \(k\) does not exis or the rank of 2 is not possible in this case
AP EAMCET-2022-06.07.2022
Matrix and Determinant
79459
A value of \(b\) for which the rank of the matrix \(A=\left[\begin{array}{cccc} 1 & 1 & -1 & 0 \\ 4 & 4 & -3 & 1 \\ b & 2 & 2 & 2 \\ 9 & 9 & b & 3 \end{array}\right] \text { is } 3 \text {, is }\)
79457
If \(a, b, c\) are the integers between 1 and 9 and a51, b41, c31 are three digit numbers and the value of determinant \(D=\left|\begin{array}{ccc}5 & 4 & 3 \\ \text { a51 } & \text { b41 } & \text { c31 } \\ a & b & c\end{array}\right|\) is zero, then \(a, b, c\) are
79458
Let \(A=\left[\begin{array}{rrrr}1 & 0 & -1 & -3 \\ 0 & 1 & 1 & k-1 \\ 0 & 0 & k-1 & 1\end{array}\right]\) and \(k \in R\). Then the value of \(k\) if exists for which the rank of \(A\) is 2 , is
1 1
2 does not exist
3 \(1 / 3\)
4 \(1,1 / 3\)
Explanation:
(B) : Given, \(A=\left[\begin{array}{llll}1 & 0 & -1 & -3 \\ 0 & 1 & 1 & \mathrm{k}-1 \\ 0 & 0 & \mathrm{k}-1 & 1\end{array}\right]\) Applying \(\mathrm{R}_{2} \rightarrow \mathrm{R}_{2}+\mathrm{R}_{3}\) \(A=\left[\begin{array}{llll} 1 & 0 & -1 & -3 \\ 0 & 1 & \mathrm{k} & \mathrm{k} \\ 0 & 0 & \mathrm{k}-1 & 1 \end{array}\right]\) The value of \(k\) does not exis or the rank of 2 is not possible in this case
AP EAMCET-2022-06.07.2022
Matrix and Determinant
79459
A value of \(b\) for which the rank of the matrix \(A=\left[\begin{array}{cccc} 1 & 1 & -1 & 0 \\ 4 & 4 & -3 & 1 \\ b & 2 & 2 & 2 \\ 9 & 9 & b & 3 \end{array}\right] \text { is } 3 \text {, is }\)
79457
If \(a, b, c\) are the integers between 1 and 9 and a51, b41, c31 are three digit numbers and the value of determinant \(D=\left|\begin{array}{ccc}5 & 4 & 3 \\ \text { a51 } & \text { b41 } & \text { c31 } \\ a & b & c\end{array}\right|\) is zero, then \(a, b, c\) are
79458
Let \(A=\left[\begin{array}{rrrr}1 & 0 & -1 & -3 \\ 0 & 1 & 1 & k-1 \\ 0 & 0 & k-1 & 1\end{array}\right]\) and \(k \in R\). Then the value of \(k\) if exists for which the rank of \(A\) is 2 , is
1 1
2 does not exist
3 \(1 / 3\)
4 \(1,1 / 3\)
Explanation:
(B) : Given, \(A=\left[\begin{array}{llll}1 & 0 & -1 & -3 \\ 0 & 1 & 1 & \mathrm{k}-1 \\ 0 & 0 & \mathrm{k}-1 & 1\end{array}\right]\) Applying \(\mathrm{R}_{2} \rightarrow \mathrm{R}_{2}+\mathrm{R}_{3}\) \(A=\left[\begin{array}{llll} 1 & 0 & -1 & -3 \\ 0 & 1 & \mathrm{k} & \mathrm{k} \\ 0 & 0 & \mathrm{k}-1 & 1 \end{array}\right]\) The value of \(k\) does not exis or the rank of 2 is not possible in this case
AP EAMCET-2022-06.07.2022
Matrix and Determinant
79459
A value of \(b\) for which the rank of the matrix \(A=\left[\begin{array}{cccc} 1 & 1 & -1 & 0 \\ 4 & 4 & -3 & 1 \\ b & 2 & 2 & 2 \\ 9 & 9 & b & 3 \end{array}\right] \text { is } 3 \text {, is }\)