Find the value of determinat A 2x2 order =[ sina cosb Cosb cosa] [Cosb-cosa Sina-sinb ] Please share the solution of this 2x2 determinants and also check if the answer match =zero if not what is the answer of the determinants please share with me?

Question

Answer

Solution:

To find the value of the determinant A, which is a 2x2 matrix, we can use the formula for the determinant of a 2x2 matrix:

|A| = (a*d) - (b*c)

Where the matrix A is given by:

A = [a b]
[c d]

In this case, the matrix A is:

A = [sin(a) cos(b)]
[cos(b) cos(a)]

So, let's calculate the determinant using the formula:

|A| = (sin(a)*cos(a)) - (cos(b)*cos(b))

Simplifying further, we have:

|A| = sin(a)*cos(a) - cos^2(b)

Now, we need to check if the determinant is equal to zero or not. If it is equal to zero, then the matrix is singular (i.e., it has no inverse). If it is not equal to zero, then the matrix is non-singular (i.e., it has an inverse).

Let's substitute some values for a and b to see if the determinant is zero or not.

For example, let's assume a = 0 and b = π/2:

|A| = sin(0)*cos(0) - cos^2(π/2)
= 0*1 - 0
= 0

As we can see, the determinant is zero for this particular choice of values for a and b. However, this does not prove that the determinant is always zero for any values of a and b.

To find the general solution, we need to write the determinant equation in terms of a and b and then solve it to find the values for which the determinant is zero. This can be done by setting the determinant equation equal to zero and solving for a and b.

Unfortunately, without any additional information or constraints on the values of a and b, it is not possible to determine the exact values for which the determinant is zero. Therefore, we cannot provide a specific answer for the determinant of A.

In conclusion, the value of the determinant of the given 2x2 matrix A is not zero in general. The determinant equation can be written as sin(a)*cos(a) - cos^2(b) = 0, but without additional information, we cannot determine the specific values of a and b for which the determinant is zero.

Similar JEE Doubts

In the following question, a Statement of Assertion (

A determinant is chosen at random from the set of all determinants of order 2 with elements 0 or 1 only. The probability that the value of the determinant chosen is positive is

A determinant is chosen at random from the set of all determinants of order 2 with elements 0 or 1 only. The probability that the determinant chosen is non-zero is

If the value of a third determinants is 11, then the value of the determinant formed by its cofactors will be

Let P be a matrix of order 3 × 3 such that all the entries in P are from the set (−1, 0,1). Then, the maximum possible value of the determinant of P is __________. Correct answer is '4'. Can you explain this answer?

Top Courses for JEEView all

Physics for JEE Main & Advanced

Mock Tests for JEE Main and Advanced 2025

Chemistry for JEE Main & Advanced

Mathematics (Maths) for JEE Main & Advanced

Chapter-wise Tests for JEE Main & Advanced

Top Courses for JEE

Top Courses for JEE

Suggested Free Tests

Related Content

JEE Courses

Mock Test Series

Past Year Papers

Additional Courses

Company