Problem 1 :
Without expanding the determinant, prove that
Problem 2 :
Show that
Problem 3 :
Prove that
Problem 4 :
Prove that
Problem 5 :
Prove that
Problem 6 :
Show that
Problem 7 :
Write the general form of a 3 × 3 skew-symmetric matrix and prove that its determinant is 0. Solution
Problem 8 :
If
prove that a, b, c are in G.P. or a is a root of ax^{2} + 2bx + c = 0. Solution
Problem 9 :
prove that
Problem 10 :
If a, b, c are p^{th}, q^{th} and r^{th} terms of an A.P, find the value of
Problem 11:
Prove that
Problem 12 :
If a, b, c are all positive, and are p^{th}, q^{th} and r^{th} terms of a G.P., show that
Problem 13 :
Find the value of
if x, y and z ≠ 1 Solution
Problem 14 :
If A =
Problem 15 :
Without expanding, evaluate the following determinants
Problem 16 :
If A is a square matrix and | A | = 2, find the value of |AA^{T}| . Solution
Problem 17 :
If A and B are square matrices of order 3 such that | A | = -1 and |B| = 3, find the value of |3AB|. Solution
Problem 18 :
If λ = - 2, determine the value of
Problem 19 :
Determine the roots of the equation
Problem 20 :
Verify that det(AB) = (det A) (det B) for
Problem 21 :
Using cofactors of elements of second row, evaluate | A |, where
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