Find the sum of the following vectors:

Show that the height of a closed right circular cylinder of given surface and maximum volume, is equal to the diameter of its base.

Using matrices, solve the following system of linear equations:

x - y + 2z = 7

3x + 4y - 5z = - 5

2x - y + 3z = 12

OR

Using elementary operations, find the inverse of the following matrix:

If write the cofactor of the element a32 .

Using properties of determinants, prove the following: