Evaluate the determinants in Exercises 1 and 2.

Evaluate the determinants in Exercises 1 and 2. (i) (ii)

If , then show that

Evaluate the determinants (I) (iii) (II) (iv)

If,find.

Find values of x, if (I) (ii)

If, then x is equalto (A) 6 (B) ±6 (C) -6 (D) 0

Using the property of determinants and without expanding, prove that:

By using properties of determinants, show that:

By using properties of determinants, show that: (i) (ii)

By using properties of determinants, show that:

By using properties of determinants, show that: (i) (ii)

By using properties of determinants, show that:

Choose the correct answer. Let A be a square matrix of order 3 ×3,thenis equalto A.B.C.D.

Which of the following is correct? (I) Determinant is a squarematrix. (II) Determinant is a number associated to amatrix. (III) Determinant is a number associated to a squarematrix. (IV) None of these

Find area of the triangle with vertices at the point given in each of the following: (i) (1, 0), (6, 0), (4, 3) (ii) (2, 7), (1, 1), (10, 8) (iii) (-2, -3), (3, 2), (-1, -8)

Show that points are collinear

Find values of k if area of triangle is 4 square units and vertices are (i) (k, 0), (4, 0), (0, 2) (ii) (-2, 0), (0, 4), (0, k)

(I) Find equation of line joining (1, 2) and (3, 6) usingdeterminants (II) Find equation of line joining (3, 1) and (9, 3) using determinants

If area of triangle is 35 square units with vertices (2, -6), (5, 4), and (k, 4). Then k is A. 12 B. -2 C. -12, -2 D. 12, -2

Write Minors and Cofactors of the elements of following determinants: (i)(ii)

(i)(ii)

Using Cofactors of elements of second row, evaluate .

Using Cofactors of elements of third column, evaluate

(i)

(ii) ' answer='

(ii)

Exercise 4.5 '>

For the matrices A and B, verify that (AB)' =where (i) (ii)

Find adjoint of each of the matrices.

Verify A (adj A) = (adj A)A=I.

Find the inverse of each of the matrices (if it exists).

Find the inverse of each of the matrices (if it exists). .

Find the inverse of each of the matrices (if it exists).

Let and . Verify that

If , show that . Hence find .

For the matrix , find the numbers a and b such that A2 + aA + bI = O.

Forthematrixshow that A³ - 6A² + 5A + 11 I = O. Hence,find A-1.

Ifverify that A³ - 6A² + 9A - 4I = O and hence findA^-1

Let A be a nonsingular square matrix of order 3 ×3.Thenis equalto A.B.C.D.

If A is an invertible matrix of order 2, then det (A^-1) is equal to A. det (A) B. C. 1 D. 0

Examine the consistency of the system of equations. x + 2y = 2 2x + 3y = 3

Examine the consistency of the system of equations. 2x - y = 5x + y = 4

Examine the consistency of the system of equations. x + 3y = 5 2x + 6y = 8

Examine the consistency of the system of equations. x + y + z = 12x + 3y + 2z = 2 ax + ay + 2az = 4

Examine the consistency of the system of equations. 3x - y - 2z = 2 2y - z =-1 3x - 5y =3

Examine the consistency of the system of equations. 5x - y + 4z = 5 2x + 3y + 5z = 2 5x - 2y + 6z = -1

Solve system of linear equations, using matrix method.

Solve system of linear equations, using matrixmethod. 5x + 2y =3 3x + 2y =5

Solve system of linear equations, using matrix method.

Solve system of linear equations, using matrix method. x - y + z = 4 2x + y - 3z =0 x + y + z = 2

Solve system of linear equations, using matrix method. 2x + 3y + 3z = 5 x - 2y + z = -4 3x - y - 2z = 3

Solve system of linear equations, using matrix method. x - y + 2z = 73x + 4y - 5z = -5 2x - y + 3z = 12

If, find A^-1. Using A^-1 solve the system ofequations

Thecostof4kgonion,3kgwheatand2kgriceisRs60.Thecostof2kgonion,4kg wheatand6kgriceisRs90.Thecostof6kgonion2kgwheatand3kgriceisRs70. Find cost of each item per kg by matrixmethod.

Prove that the determinant is independent of ?.

Without expanding the determinant, prove that