NCERT Exemplar Solutions
Class 12 - Mathematics - Chapter 4: DETERMINANTS

Fill in the Blanks

If A is a matrix of order 3 × 3, then |3A| = ____.

If A is an invertible matrix of order 3 × 3, then |A⁻¹| = ____.

If x, y, z ∈ R, then the value of determinant

\( \begin{vmatrix} (2^x + 2^{-x})^2 & (2^x - 2^{-x})^2 & 1 \\ (3^x + 3^{-x})^2 & (3^x - 3^{-x})^2 & 1 \\ (4^x + 4^{-x})^2 & (4^x - 4^{-x})^2 & 1 \end{vmatrix} \)

is equal to ____.

If cos 2θ = 0, then

\( \begin{vmatrix} 0 & \cos \theta & \sin \theta \\ \cos \theta & \sin \theta & 0 \\ \sin \theta & 0 & \cos \theta \end{vmatrix} \)

= ____.

If A is a matrix of order 3 × 3, then (A²)⁻¹ = ____.

If A is a matrix of order 3 × 3, then number of minors in determinant of A are ____.

The sum of the products of elements of any row with the co-factors of corresponding elements is equal to ____.

If x = −9 is a root of

\( \begin{vmatrix} x & 3 & 7 \\ 2 & x & 2 \\ 7 & 6 & x \end{vmatrix} = 0 \)

, then other two roots are ____.

\( \begin{vmatrix} 0 & xyz & x - z \\ y - x & 0 & y - z \\ z - x & z - y & 0 \end{vmatrix} = \\ ____.

If

\( f(x) = \begin{vmatrix} (1+x)^{17} & (1+x)^{19} & (1+x)^{23} \\ (1+x)^{23} & (1+x)^{29} & (1+x)^{34} \\ (1+x)^{41} & (1+x)^{43} & (1+x)^{47} \end{vmatrix} = A + Bx + Cx^2 + \ldots \)

then A = ____.