Give an example of a 2x2 matrix whose determinant is 13.

How would I come up with numbers? Is it just a random guess and check?

Question

Give an example of a 2x2 matrix whose determinant is 13.

How would I come up with numbers? Is it just a random guess and check?

jim_thompson5910 · Answer

If you have the 2x2 matrix

a      b
c      d

The determinant D is D = ad - bc

anonymous · Answer

How can I put that into actual numbers?

anonymous · Answer

1    0
0    a 
What is the deterninant?

anonymous · Answer

13

anonymous · Answer

1   0
0   13

anonymous · Answer

Nice lol. So is it just a guess and check?

anonymous · Answer

There are a lot of matrices that have determinant 13

jim_thompson5910 · Answer

no, just fix 3 values and make the fourth value unknown and solve for it

anonymous · Answer

Yes an infinite number of matrices have determinant 13.

anonymous · Answer

What if you get a decimal?

anonymous · Answer

1    1
1    14

anonymous · Answer

How can you make sure that you don't get a decimal?

anonymous · Answer

1   2
1   15

anonymous · Answer

1   3
1   16

anonymous · Answer

1  4
1   17

anonymous · Answer

ok dude thanks, but how do you make sure you don't get a decimal? How are you coming up with so many

anonymous · Answer

If all your entries are integers, the determinant is an integer.

anonymous · Answer

1   17
   1   30

jim_thompson5910 · Answer

The determinant is D = ad - bc


Fix values for a, b, and c. Say a = 2, b = 3, and c = 4 (these values are completely random)


D = ad - bc

13 = 2d - 3*4

13 = 2d - 12

13+12 = 2d

25 = 2d

25/2 = d

d = 12.5

So 

2         3
4        12.5


has a determinant of 13

anonymous · Answer

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