Write a 3 x 3..... (Elementary Algebra)

Question

Ques. >> Write 3 x 3 sq. matrix A whose determent is 75.... show steps if possible

Answer 1

 The simplest 3X3 matrix is:

( 75 0 0 )

( 0 1 0 )

( 0 0 1 ) 

because the only non-zero component of the determinant is 75*(1*1-0*0)=75. The remaining components have zero multipliers.

Comments

Thank you so much for your help.... But would this be enough for a 4 mark question??

---

Sometimes simplest is best. The question only asks for one example, and that's what's been given. If the question had asked for two examples, I think that would have been worth more than 4 marks. Some marks are given for what is invisible, like ingenuity. Only the results of a thought process can be written down, and that thought process could take up a lot of time, but result in a short answer. You know how best to judge how the marking works. Let see what your teachers think! Best wishes.

---

Another example is A=

( 3 0 0 )

( 0 5 0 )

( 0 0 5 )

or

( 0 5 0 )

( 0 0 3 )

( 5 0 0 ) |A|=-5(0-3*5)=75