(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

If $x, y, z$ are not all simultaneously equal to zero,satisfying the system of equations
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$2 x + 7 y + 7 z = 0$
then the number of principal values of $\theta$ is

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EasyKCET 2015

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The area of the triangle whose vertices are $(3,5), (2,2)$ and $(k, 2)$ is $3$ sq. unit. Then,the value of $k$ is . . . . . . .

EasyGSEB 2024

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If $a, b, c$ are in $A.P.$,then the determinant $\left|\begin{array}{lll}x+2 & x+3 & x+2a \\ x+3 & x+4 & x+2b \\ x+4 & x+5 & x+2c\end{array}\right|$ is

Medium

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If $A = \begin{bmatrix} 5 & 5x & x \\ 0 & x & 5x \\ 0 & 0 & 5 \end{bmatrix}$ and $|A^2| = 25$, then $|x|$ is equal to

EasyWBJEE 2019

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If $x, y, z$ are not all simultaneously equal to zero,satisfying the system of equations$(\sin 3 \theta) x - y + z = 0$$(\cos 2 \theta) x + 4 y + 3 z = 0$$2 x + 7 y + 7 z = 0$then the number of principal values of $\theta$ is

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The area of the triangle whose vertices are $(3,5), (2,2)$ and $(k, 2)$ is $3$ sq. unit. Then,the value of $k$ is . . . . . . .

If $a, b, c$ are in $A.P.$,then the determinant $\left|\begin{array}{lll}x+2 & x+3 & x+2a \\ x+3 & x+4 & x+2b \\ x+4 & x+5 & x+2c\end{array}\right|$ is

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If $x, y, z$ are not all simultaneously equal to zero,satisfying the system of equations
$(\sin 3 \theta) x - y + z = 0$
$(\cos 2 \theta) x + 4 y + 3 z = 0$
$2 x + 7 y + 7 z = 0$
then the number of principal values of $\theta$ is