Using the properties of determinants in evaluate:
Using the properties of determinants in prove that:
If A + B + C = 0, then prove that
If the co-ordinates of the vertices of an equilateral triangle with sides of length ‘a’ are (x1, y1), (x2, y2), (x3, y3), then
Find the value of θ satisfying
If then find values of x.
If a1, a2, a3, ..., ar are in G.P., then prove that the determinant is independent of r.
Show that the points (a + 5, a – 4), (a – 2, a + 3) and (a, a) do not lie on a straight line for any value of a.
Show that the Δ ABC is an isosceles triangle if the determinant
Find A–1 if and show that
If find A–1. Using A–1, solve the system of linear equations x – 2y = 10, 2x – y – z = 8, –2y + z = 7.
Using matrix method, solve the system of equations 3x + 2y – 2z = 3, x + 2y + 3z = 6, 2x – y + z = 2
Given find BA and use this to solve the system of equations y + 2z = 7, x – y = 3, 2x + 3y + 4z = 17.
If a + b + c ≠ 0 and then prove that a = b = c.
Prove that is divisible by a + b + c and find the quotient.
If x + y + z = 0, prove that
If then value of x is
The value of determinant
The area of a triangle with vertices (–3, 0), (3, 0) and (0, k) is 9 sq. units. The value of k will be
The determinant equals
The number of distinct real roots of in the interval is
If A, B and C are angles of a triangle, then the determinant is equal to
Let then is equal to
The maximum value of is (θ is a real number)
If ,
If , then A-1 exists if
If A and B are invertible matrices, then which of the following is not correct?
If x, y, z are all different from zero and , then value of x-1 + y-1 + z-1 is
The value of the determinant is
There are two values of a which makes determinant, ,then sum of these number is
Fill in the blanks
If A is a matrix of order 3 × 3, then |3A| = ___.
If A is invertible matrix of order 3 × 3, then |A-1|= ____.
If x, y, z ∈ R, then the value of determinant is equal to ___.
If cos 2θ = 0, then
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 , then other two roots are ___.
If , then A = ____.
State True or False for the statements
(A3)-1 = (A-1)3, where A is a square matrix and |A| ≠ 0.
(aA)-1 = (1/a) A-1, where a is any real number and A is a square matrix.
|A-1| ≠ |A|-1, where A is non-singular matrix.
If A and B are matrices of order 3 and |A| = 5, |B| = 3, then |3AB| = 27 × 5 × 3 = 405.
If the value of a third order determinant is 12, then the value of the determinant formed by replacing each element by its co-factor will be 144.
, where a, b, c are in A.P.
|adj. A| = |A|2, where A is a square matrix of order two.
The determinant is equal to zero.
If the determinant splits into exactly K determinants of order 3, each element of which contains only one term, then the value of K is 8.
Let ,then
The maximum value of is 1/2.
