find the determinant of a 2x2 matrix ,matrix multiplication 2x2, Evaluate the determinants in Exercises 1 and 2

find the determinant of a 2x2 matrix ,matrix multiplication 2x2
Evaluate the determinants in Exercises 1 and 2.

Answer

Use formula

    = 2(−1) − 4(−5) = − 2 + 20 = 18

Question 2:

Evaluate the determinants in Exercises 1 and 2.

Answer

Use formula

 = (cos θ)(cos θ) − (−sin θ)(sin θ) = cos² θ+ sin² θ = 1

(ii)

Use formula

= (x² − x + 1)(x + 1) − (x − 1)(x + 1)

= x³ − x² + x + x² − x + 1 − (x² − 1)

= x³ + 1 − x² + 1

= x³ − x² + 2

3. If

, then show that | 2A | = 4 | A |

LHS

                        =2(4) – 4(8)

   = 8 – 32

   =  - 24 

R.H.S

                         = 4(2 – 8)

                         = 4(-6)

                         = - 24

L.H.S = R.H.S

Hence proved

4. If

 , then show that | 3 A | = 27 | A |

LHS

Use formula

=>|3A| =  3(36 - 0) – 0(0 -0) + 3(0-0)

            = 108

R.H.S

  

= 27 x 4

= 108

LHS = RHS

Hence proved