NCERT Solutions for Class 12-science Maths Chapter 3 - Matrices

Chapter 3 - Matrices Ex. 3.1

Solution 1
Solution 2
Solution 3
Solution 4

Let A =

(i)

a11 =  ,

a12 =  ,

a21 =  ,

a22 =

Therefore, A =

(ii)

a11 =  ,

a12 =  ,

a21 =  ,

a22 =

Therefore, A =

(iii)

a11 =  ,

a12 =  ,

a21 =  ,

a22 =

Therefore, A =  . 

Solution 5

Solution 6

Solution 7
Solution 8
Solution 9

Solution 10

Chapter 3 - Matrices Ex. 3.2

Solution 1

Solution 2
Solution 3


(i) begin mathsize 12px style open square brackets table row straight a straight b row cell negative straight b end cell straight a end table close square brackets end stylebegin mathsize 12px style open square brackets table row straight a cell negative straight b end cell row straight b straight a end table close square brackets end style

begin mathsize 12px style equals open square brackets table row cell straight a squared plus straight b squared end cell cell negative ab plus ab end cell row cell negative ab plus ab end cell cell straight b squared plus straight a squared end cell end table close square brackets end style

begin mathsize 12px style equals open square brackets table row cell straight a squared plus straight b squared end cell 0 row 0 cell straight a squared plus straight b squared end cell end table close square brackets end style

ii)begin mathsize 12px style open square brackets table row 1 row 2 row 3 end table close square brackets open square brackets table row 2 3 4 end table close square brackets end style

begin mathsize 12px style equals open square brackets table row 2 3 4 row 4 6 8 row 6 9 12 end table close square brackets end style

iii)begin mathsize 12px style open square brackets table row 1 cell negative 2 end cell row 2 3 end table close square brackets space open square brackets table row 1 2 3 row 2 3 1 end table close square brackets end style

begin mathsize 12px style equals open square brackets table row cell 1 minus 4 end cell cell 2 minus 6 end cell cell 3 minus 2 end cell row cell 2 plus 6 end cell cell 4 plus 9 end cell cell 6 plus 3 end cell end table close square brackets end style

begin mathsize 12px style equals open square brackets table row cell negative 3 end cell cell negative 4 end cell 1 row 8 13 9 end table close square brackets end style

iv)begin mathsize 12px style open square brackets table row 2 3 4 row 3 4 5 row 4 5 6 end table close square brackets space space open square brackets table row 1 cell negative 3 end cell 5 row 0 2 4 row 3 0 5 end table close square brackets end style

begin mathsize 12px style equals open square brackets table row cell 2 plus 0 plus 12 end cell cell negative 6 plus 6 plus 0 end cell cell 10 plus 12 plus 20 end cell row cell 3 plus 0 plus 15 end cell cell negative 9 plus 8 plus 0 end cell cell 15 plus 16 plus 25 end cell row cell 4 plus 0 plus 18 end cell cell negative 12 plus 10 plus 0 end cell cell 20 plus 20 plus 30 end cell end table close square brackets end style

begin mathsize 12px style equals open square brackets table row 14 0 42 row 18 cell negative 1 end cell 56 row 22 cell negative 2 end cell 70 end table close square brackets end style

v)begin mathsize 12px style open square brackets table row 2 1 row 3 2 row cell negative 1 end cell 1 end table close square brackets open square brackets table row 1 0 1 row cell negative 1 end cell 2 1 end table close square brackets end style

begin mathsize 12px style equals open square brackets table row cell 2 minus 1 end cell cell 0 plus 2 end cell cell 2 plus 1 end cell row cell 3 minus 2 end cell cell 0 plus 4 end cell cell 3 plus 2 end cell row cell negative 1 minus 1 end cell cell negative 0 plus 2 end cell cell negative 1 plus 1 end cell end table close square brackets end style

begin mathsize 12px style equals open square brackets table row 1 2 3 row 1 4 5 row cell negative 2 end cell 2 0 end table close square brackets end style

vi)begin mathsize 12px style open square brackets table row 3 cell negative 1 end cell 3 row cell negative 1 end cell 0 2 end table close square brackets open square brackets table row 2 cell negative 3 end cell row 1 0 row 3 1 end table close square brackets end style

begin mathsize 12px style equals open square brackets table row cell 6 minus 1 plus 9 end cell cell negative 9 plus 0 plus 3 end cell row cell negative 2 plus 0 plus 6 end cell cell 3 plus 0 plus 2 end cell end table close square brackets end style

begin mathsize 12px style equals open square brackets table row 14 cell negative 6 end cell row 4 5 end table close square brackets end style

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

Solution 19

Solution 20
Solution 21
Solution 22

Chapter 3 - Matrices Ex. 3.3

Solution 1
Solution 2

Solution 3

Solution 4
Solution 5

Solution 6(i)

Solution 6(ii)

Solution 7
Solution 8
Solution 9

Solution 10



Solution 11
Solution 12

Chapter 3 - Matrices Ex. 3.4

Solution 1
Solution 2
Solution 3
Solution 4
Solution 5
Solution 6

Solution 7

Solution 8
Solution 9
Solution 10

Let A =

Now, det(A)=|A|=6-4=2≠0

Therefore, inverse of A exist.

We know that, A=AI

  ….. (C2C2+ C1)

  ….. (C1C1+6C2)

  ….. (C1 C1)

  ….. (C2 C2)

  

Solution 11

Solution 12
Solution 13
Solution 14
Solution 15

Solution 16

Solution 17

Solution 18

Chapter 3 - Matrices Misc. Ex.

Solution 1



Solution 2

Solution 3

Solution 4
Solution 5

Solution 6
Solution 7
Solution 8
Solution 9
Solution 10

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Solution 11


Solution 12

Solution 13
Solution 14
Solution 15