NCERT Solutions for Class 12-science Maths Chapter 4 - Determinants

Chapter 4 - Determinants Ex. 4.1

Solution 1
Solution 2
Solution 3
Solution 4

Solution 5

Solution 6
Solution 7
Solution 8

Chapter 4 - Determinants Ex. 4.2

Solution 1

Solution 2

Solution 3

Solution 4

Solution 5

Solution 6

Solution 7

Solution 8

Solution 9

A p p l y i n g space R subscript 3 rightwards arrow R subscript 2 plus R subscript 3 comma space w e space h a v e
capital delta equals open parentheses x minus y close parentheses open parentheses z minus x close parentheses open vertical bar table row x cell x squared end cell cell y z end cell row cell minus 1 end cell cell minus x minus y end cell z row 0 cell z minus y end cell cell z minus y end cell end table close vertical bar
rightwards double arrow capital delta equals open parentheses x minus y close parentheses open parentheses z minus x close parentheses open parentheses z minus y close parentheses open vertical bar table row x cell x squared end cell cell y z end cell row cell minus 1 end cell cell minus x minus y end cell z row 0 1 1 end table close vertical bar
rightwards double arrow capital delta equals minus open parentheses x minus y close parentheses open parentheses z minus x close parentheses open parentheses z minus y close parentheses open vertical bar table row x cell x squared end cell cell y z end cell row 1 cell x plus y end cell cell minus z end cell row 0 1 1 end table close vertical bar
rightwards double arrow capital delta equals open parentheses x minus y close parentheses open parentheses z minus x close parentheses open parentheses y minus z close parentheses open vertical bar table row x cell x squared end cell cell y z end cell row 1 cell x plus y end cell cell minus z end cell row 0 1 1 end table close vertical bar
rightwards double arrow capital delta equals open parentheses x minus y close parentheses open parentheses z minus x close parentheses open parentheses y minus z close parentheses open square brackets x open parentheses x plus y close parentheses plus x z minus x squared plus y z close square brackets
rightwards double arrow capital delta equals open parentheses x minus y close parentheses open parentheses z minus x close parentheses open parentheses y minus z close parentheses open square brackets x squared plus x y plus x z minus x squared plus y z close square brackets
rightwards double arrow capital delta equals open parentheses x minus y close parentheses open parentheses z minus x close parentheses open parentheses y minus z close parentheses open square brackets x y plus x z plus y z close square brackets
H e n c e space p r o v e d.

Solution 10

Solution 11

Solution 12
Solution 13

Solution 14

Solution 15

Solution 16

Chapter 4 - Determinants Ex. 4.3

Solution 1

Solution 2

Solution 3

Solution 4

Solution 5

Chapter 4 - Determinants Ex. 4.4

Solution 1

Solution 2

Solution 3

Solution 4

Solution 5

Chapter 4 - Determinants Ex. 4.5

Solution 1

Solution 2

Solution 3

Solution 4

Solution 5

Solution 6

Solution 7

Solution 8

Solution 9

Solution 10

Solution 11

Solution 12

Solution 13

Solution 14

Solution 15

Solution 16

Solution 17

Solution 18

Chapter 4 - Determinants Ex. 4.6

Solution 1

Solution 2

Solution 3

Solution 4

Solution 5

Solution 6

Solution 7

Solution 8

Solution 9

Solution 10

Solution 11

Solution 12

Solution 13

Solution 14

Solution 15

Solution 16

x = 5, y = 8 and z = 8

Hence, the cost of onion per kg is Rs. 5, the cost of wheat per kg is Rs. 8 and the cost of rice per kg is Rs. 8.

Chapter 4 - Determinants Misc. Ex.

Solution 15

Solution 1

Solution 2

Solution 3

Solution 4

Solution 5

Solution 6

Solution 7

Solution 8

Solution 9

Solution 10

Solution 11

Solution 12

Solution 13

Solution 14
Solution 16

Solution 17

Solution 18

Solution 19