NCERT Solutions for Class 12-commerce Maths CBSE Chapter 3: Matrices

Matrices Exercise 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

Matrices Exercise Ex. 3.2

Solution 1

Solution 2

Solution 3

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

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

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

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

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