Use the concept of volume to explain why the determinant of a 3×3 matrix a is zero if and only if a is not invertible. what must be done to prove that the determinant of a 3×3 matrix a is zero if and only if a is not invertible?

See explanation below

Step-by-step explanation:

On this case what we need to proof is:

"If the matrix A is not invertible then the determinant is 0"

Let A the matrix of interest. If the matrix is not invertible then

Let denote the inverse of A as

If the matrix is not invertible we have this:

And taking determinant in both sides we get:

And using propoerties of determinants we got:

A 3x3 matrix A is not invertible if and only if its columns are linearly independent.

And if the columns are linearly indpendent then the determinant is 0. And we can associate this to the volume with the following theorem

"Let  v 1 , v 2 ,..., v n  be vectors in  R n ,  let  P  be the parallelepiped determined by these vectors, and let  A  be the matrix with rows  v 1 , v 2 ,..., v n .  Then the absolute value of the determinant of  A  is the volume of  P."

And if one vector is linear dependnet we have that the detemrinant would be 0 and the matrix would not invertible

the total estimated nappy use.=10,500,000

step-by-step explanation:

given that on an average the average baby uses 3528 napkins.

in a particular year 2014, the number of births were 299697 in new south wales.

rounding off the number of births to the nearest hundred thousand we have

no of birtsh = 300000

also rounding off the average usage to nearst thousand we get

average use of a baby = 3500

hence total number of nappy estimated to be used = 3500x300000

= 10,500,000

answer is 10,500,000 nappies

step-by-step explanation:

well if you round, things become much more simple. round 5.95 to 6, 4.25 to 4, and 1.05 to 1. now, add 6+4+1 and that would equal 11. so the items together would equal to about $11.