(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 3-4. Matrices and Determinants 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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3-4. Matrices and Determinants

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

If $a+b+c= S$,then the value of $\left|\begin{array}{ccc} S+c & a & b \\ c & S+a & b \\ c & a & S+b \end{array}\right|$ is . . . . . . .

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The value of $k$ for which the set of equations $x + ky + 3z = 0, 3x + ky - 2z = 0, 2x + 3y - 4z = 0$ has a non-trivial solution over the set of rationals is

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If the determinant of the matrix $A = \begin{bmatrix} 0 & a & b \\ -a & 0 & \beta \\ -b & -\alpha & 0 \end{bmatrix}$ is zero for all $a, b$, then $\alpha + \beta =$

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The matrix $\left[ {\begin{array}{*{20}{c}}2&\lambda &{ - 4}\\{ - 1}&3&4\\1&{ - 2}&{ - 3}\end{array}} \right]$ is non-singular,if

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If the coordinates of the points $A, B,$ and $C$ are $(4, 4), (3, -2),$ and $(3, -16)$ respectively,then the area of the triangle $ABC$ is

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If $a+b+c= S$,then the value of $\left|\begin{array}{ccc} S+c & a & b \\ c & S+a & b \\ c & a & S+b \end{array}\right|$ is . . . . . . .

The value of $k$ for which the set of equations $x + ky + 3z = 0, 3x + ky - 2z = 0, 2x + 3y - 4z = 0$ has a non-trivial solution over the set of rationals is

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