SOLVED PROBLEMS ON DETERMINANTS

About "Solved Problems on Determinants"

Solved Problems on Determinants :

Here we are going to see some practice problems on determinants.

Solved Problems on Determinants - Practice Questions

Question 1 :

Without expanding the determinant, prove that Solution

Question 2 :

Show that Solution

Question 3 :

Prove that Solution

Question 4 :

Prove that Solution

Question 5 :

Prove that Solution

Question 6 :

Show that Solution

Question 7 :

Write the general form of a 3 × 3 skew-symmetric matrix and prove that its determinant is 0.    Solution

Question 8 :

If prove that a, b, c are in G.P. or a is a root of ax2 + 2bx + c = 0.             Solution

Question 9 :

prove that Solution

Question 10 :

If a, b, c are pth, qth and rth terms of an A.P, find the value of Solution

Question 11:

Prove that Solution

Question 12 :

If a, b, c are all positive, and are pth, qth and rth terms of a G.P., show that Solution

Question 13 :

Find the value of if x, y and z ≠ 1       Solution

Question 14 :

If A = Solution

Question 15 :

Without expanding, evaluate the following determinants  Solution

Question 16 :

If A is a square matrix and | A | = 2, find the value of |AAT| .                 Solution

Question 17 :

If A and B are square matrices of order 3 such that | A | = -1 and |B| = 3, find the value of |3AB|.      Solution

Question 18 :

If λ = - 2, determine the value of Solution

Question 19 :

Determine the roots of the equation Solution

Question 20 :

Verify that det(AB) = (det A) (det B) for Solution

Question 21 :

Using cofactors of elements of second row, evaluate | A |, where Solution After having gone through the stuff given above, we hope that the students would have understood, "Solved Problems on Determinants".

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