Q6 of 26 Page 1

Find the integrating factor of the differential equation

We have,

Which is a linear differential equation of the type

Write the element a₂₃ of a 3 × 3 matrix A = (a_jj) whose elements a_ij are given by

Find the differential equation representing the family of curves where A and B are arbitrary constants.

If a = ( ccc 2&0&1 2&1&3 1&-1&0 ) find A² – 5A + 4I and hence find a matrix X such that A² – 5A + 4I + X = O.

If a = [ ccc 1&-2&3 0&-1&4 -2&2&1 ] find (A’)^-1.

If using properties of determinants find the value of f(2x) – f(x).