and A3 = 125, then find a 3 What is the value of a11A11+ a12A12+ a13A13 with respect to determinant A of order 3 4 A and B are square matrix of order 3
| Previous PDF | Next PDF |
[PDF] Determinants - NCERT
complex) called determinant of the square matrix A, where aij = (i, j)th element of Step 2 Multiply 2nd element a12 of R1 by (–1)1 + 2 [(–1)sum of suffixes in a In earlier classes, we have studied that the area of a triangle whose vertices are
[PDF] Matrices - NCERT
The knowledge of matrices is necessary in various branches of mathematics Solution In general a 3 × 2 matrix is given by 11 12 21 22 31 32 A a a a a
[PDF] Chapter 9 Matrices and Determinants - PBTE
It is denoted by det A or A for a square matrix A The determinant of the (2 x 2) matrix A = 11 12 21 22
[PDF] CHAPTER 8: MATRICES and DETERMINANTS
The material in this chapter will be covered in your Linear Algebra class (Math 254 at Mesa) SECTION 8 1: MATRICES and SYSTEMS OF EQUATIONS PART A:
[PDF] Mathematics Notes for Class 12 chapter 4 Determinants - Ncert Help
Every square matrix A is associated with a number, called its determinant and it is denoted by det (A) or A Only square matrices have determinants The matrices
[PDF] Mathematics Notes for Class 12 chapter 3 Matrices - Ncert Help
16 Singular Matrix A square matrix A is said to be singular matrix, if determinant of A denoted by det (A) or A is
[PDF] Class XII Chapter 4 - DETERMINANTS Worksheet – Module 4/4
and A3 = 125, then find a 3 What is the value of a11A11+ a12A12+ a13A13 with respect to determinant A of order 3 4 A and B are square matrix of order 3
[PDF] C H A P T E R 8 Matrices and Determinants
Applications of Matrices and Determinants 12 7 2 Vocabulary Check 1 matrix 2 square 3 main diagonal 4 row Message: CLASS IS CANCELED 9
[PDF] Notes on Mathematics - 102 - For IIT Kanpur
12 CHAPTER 1 MATRICES 1 2 1 Multiplication of Matrices Definition 1 2 8 Definition 2 8 2 (Determinant of a Square Matrix) Let A be a square matrix of order context, we have a class of equations, called Linear Equations (to be defined
[PDF] MATRICES - NIOS
m × n matrix, the element a ij belongs to the ith row and jth column 11 12 13 In this lesson, we will learn various properties of determinants and also In earlier classes, you have learnt how to solve linear equations in two or three unknowns
[PDF] matrices and determinants worksheets pdf
[PDF] matrices calculator rref
[PDF] matrices simultaneous equations worksheet
[PDF] matrices word problems with solutions pdf
[PDF] matrics consensus cognitive battery
[PDF] matrix bijective mapping
[PDF] matrix bipartite graph r
[PDF] matrix generator
[PDF] matrix injective
[PDF] matrix inverse 2x2 calculator
[PDF] matrix inverse method
[PDF] matrix multiplication c++
[PDF] matrix multiplication calculator 2x2
[PDF] matrix multiplication calculator 3x3
Class XII
Chapter 4 - DETERMINANTS
Worksheet Module 4/4
MCQ/One mark Questions
1 Given a square matrix A of order 3x3 such that |A| = 12. Find the value of |A adjA|.
2 If A =ቂܽ
3 What is the value of a11A11+ a12A12+ a13A13 with respect to determinant A of order 3
4 A and B are square matrix of order 3 such that |A| =2 and |B|= 3, then find |3AB|.
5 If for any 2 x 2 square matrix A, A(adjA) = ቂͲ
Ͳቃ, then write the value of |A|.
6 If A is a square matrix of order 3 and ȁ͵ܣȁ = kȁܣ
Two mark Questions
7Let A =
൩ , then find the value of Ȝ-1 exists.8 Find the values of k, if the area of a triangle is 4 sq. units and vertices are (k, 0 ), (4, 0 )and (0,2).
9 Without expanding the determinant at any stage, prove that อ
อ = 0.Four/Six marks Questions
10 If്്ܾܽܿ
อൌͲ ,then using the properties of determinants, prove that ܾܽܿ11 Find the inverse of the matrix ܣ
13 Using properties of determinants, prove that
14 Let A=ቂʹ͵
Hence solve the following system of Equations : 2x+y = 4, 3x+2y =1.15 Using matrices, solve the following system of linear equations:
2x െy + z = 3 , െx + 2y െz = െ 4 and xെy + 2z = 1
16If A-1 =
൩ and B = ൩ find (AB)-1 17Using properties of determinants, prove that
18 If a, b, c are all positive and the pth, qth, rth terms of a G.P respectively, then prove that
ቮ = 0.19 Using properties of determinants show that:
3 333 a a b a c b a b b c a b c ab bc ca c a c b c
20 Using matrix method, solve the following system of linear equations:
21 If A =
൩, then find A-1 and hence solve the following system of equations 3x + 4y + 7z = 14 ,2x y + 3z = 4, x + 2y 3z = 022 Two schools A and B decided to award prizes to their students for three values Honesty,
Punctuality and Obedience. School A decided to award a total of Rs 2200 for the three values to 3,2 and 1 students respectively, while school B decided to award Rs 3100 for the three values to 4,1
and 3 students respectively. If the three prizes per person amount to Rs 1200,using matrices, find the award prizes for each value.23 Two institutions decided to award their employees for the three values of resourcefulness,
competence and determination in the form of prices at the rate of ൟx, ൟy, and ൟz respectively per
person. The first institution decided to award respectively 4,3 and 2 employees with a total prize money of ൟ37000 and the second institution decided to award respectively 5,3 and 4 employeeswith a total prize money of ൟ47000.If all the three prizes per person together amount to ൟ 12000 ,
then using matrix method find the values of x, y and z. What values are described in this question?