Find the value of the determinant of the matrix [[2, 4], [-1, 2]].

C. 8 — To find the determinant of a 2x2 matrix, subtract the product of the secondary diagonal elements from the product of the primary diagonal elements.

JEE Main · MathematicsEasy

$Find the value of the determinant of the matrix (2 - 1 42) .$

A. $0$
B. $4$
C. $8$
D. $12$

Show correct answer & step-by-step solution

Correct answer: C — $8$

Solution

$For a matrix (a c b d), the determinant is calculated using the formula a d - b c .$
$Identify the values from the given matrix (2 - 1 42), where a = 2, b = 4, c = - 1, and d = 2 .$
$Substitute these values into the formula: (2 \times 2) - (4 \times - 1) .$
$Simplify the expression to get $4 - (-4)$, which equals $4 + 4 = 8$.$
$Hence the answer is (C).$

Attempt this question & track your score

Attempt & Track Free →

More Matrices & Determinants practice questions

$What is the value of the determinant of an identity matrix of order 3?$
$If A is a square matrix such that A squared equals A, then A is called what?$
$If a matrix A has 12 elements, what are the possible orders it can have?$
$If the matrix A = [[0, 5], [5, 0]], find A transpose.$
$I f A = [[cos t h e t a, - s in t h e t a], [s in t h e t a, cos t h e t a]], t h e n A^{n} i se q u a l t o :$
$I f A i s a 3 x 3 ma t r i x s u c h t ha t A^{2} = A an d I i s t h e i d e n t i t y ma t r i x, t h e n t h e v a l u eo f (I + A)^{n} i se q u a l t o :$
$If the system of equations x + y + z = 6, x + 2y + 3z = 10, and x + 2y + lambda z = mu has no solution, then:$
$I f A i s a s q u a r e ma t r i x s u c h t ha t A^{T} A = I, t h e n t h e d e t er minan t o f A i s :$
$T h e v a l u eo f t h e d e t er minan t o f t h e ma t r i x [[1, a, a^{2}], [1, b, b^{2}], [1, c, c^{2}]] i s :$
$L e t A b e a 3 x 3 ma t r i x s u c h t ha t A^{2} = I an d A i s n o t e q u a l t o I or - I . I f t h e t r a ceo f A i s 1, f in d t h e d e t er minan t o f A$
$If the system of equations x + y + z = 6, x + 2y + 3z = 10, and x + 2y + kz = m has no solution, then:$
$L e t A b e a 3 x 3 ma t r i x s u c h t ha t A^{T} A = I an dd e t (A) = 1. T h e n d e t (A - I) i se q u a l t o :$

View all Matrices & Determinants questions →

Find the value of the determinant of the matrix (2−1​42​).

Solution

Attempt this question & track your score

More Matrices & Determinants practice questions

$Find the value of the determinant of the matrix (2 - 1 42) .$