(D) We know that for every square matrix $A = [a_{ij}]$ of order $n$,we can associate a unique number called the determinant of the square matrix $A$,

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Determinant is a number associated to a square matrix.

(D) We know that for every square matrix $A = [a_{ij}]$ of order $n$,we can associate a unique number called the determinant of the square matrix $A$,where $a_{ij}$ is the $(i, j)^{\text{th}}$ element of $A$. Thus,the determinant is a number associated with a square matrix. Hence,the correct answer is $D$.

Class 12 Mathematics 3 and 4 .Determinants and Matrices Expansion of determinants, Solution of equation in the form of determinants and area of triangle and Equation of Line

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Which of the following is correct?

A
Determinant is a square matrix.
B
Determinant is a number associated to a matrix.
C
None of these.
D
Determinant is a number associated to a square matrix.

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3 and 4 .Determinants and Matrices

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Expansion of determinants, Solution of equation in the form of determinants and area of triangle and Equation of Line

The determinant $\left| \begin{array}{ccc} a & b & a\alpha + b \\ b & c & b\alpha + c \\ a\alpha + b & b\alpha + c & 0 \end{array} \right| = 0$,if $a, b, c$ are in

MediumIIT 1986

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If $a, b, c$ are respectively the $p^{th}, q^{th}, r^{th}$ terms of an $A.P.$,then $\left| \begin{array}{ccc} a & p & 1 \\ b & q & 1 \\ c & r & 1 \end{array} \right| = $

Medium

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If $\left[\begin{array}{ccc}1 & -1 & x \\ 1 & x & 1 \\ x & -1 & 1\end{array}\right]$ has no inverse,then the real value of $x$ is

EasyAP EAMCET 2009

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If $a_i^2 + b_i^2 + c_i^2 = 1$ for $(i = 1, 2, 3)$ and $a_i a_j + b_i b_j + c_i c_j = 0$ for $(i \ne j, i, j = 1, 2, 3)$,then the value of $\left| \begin{array}{ccc} a_1 & a_2 & a_3 \\ b_1 & b_2 & b_3 \\ c_1 & c_2 & c_3 \end{array} \right|^2$ is

Difficult

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$\left|\begin{array}{ccc} \log e & \log e^2 & \log e^3 \\ \log e^2 & \log e^3 & \log e^4 \\ \log e^3 & \log e^4 & \log e^5 \end{array}\right| \text{ is equal to: }$

EasyTS EAMCET 2006

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The determinant $\left| \begin{array}{ccc} a & b & a\alpha + b \\ b & c & b\alpha + c \\ a\alpha + b & b\alpha + c & 0 \end{array} \right| = 0$,if $a, b, c$ are in

If $a, b, c$ are respectively the $p^{th}, q^{th}, r^{th}$ terms of an $A.P.$,then $\left| \begin{array}{ccc} a & p & 1 \\ b & q & 1 \\ c & r & 1 \end{array} \right| = $

If $\left[\begin{array}{ccc}1 & -1 & x \\ 1 & x & 1 \\ x & -1 & 1\end{array}\right]$ has no inverse,then the real value of $x$ is

If $a_i^2 + b_i^2 + c_i^2 = 1$ for $(i = 1, 2, 3)$ and $a_i a_j + b_i b_j + c_i c_j = 0$ for $(i \ne j, i, j = 1, 2, 3)$,then the value of $\left| \begin{array}{ccc} a_1 & a_2 & a_3 \\ b_1 & b_2 & b_3 \\ c_1 & c_2 & c_3 \end{array} \right|^2$ is

$\left|\begin{array}{ccc} \log e & \log e^2 & \log e^3 \\ \log e^2 & \log e^3 & \log e^4 \\ \log e^3 & \log e^4 & \log e^5 \end{array}\right| \text{ is equal to: }$

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