Two schools A and B want to award their selected students on the values of sincerity, truthfulness and helpfulness. The school A wants to award x each, y each and z each for the three respective values to 3, 2 and 1 students respectively with a total award money of 1,600. School B wants to spend 2,300 to award its 4, 1 and 3 students on the respective values (by giving the same award money to the three values as before). If the total amount for one prize on each value is 900, using matrices, find the award money for each value. Apart from these three values, suggest one more value which should be considered for award.

Find the value of a if 

If  then find the matrix A. 

185.

A school wants to award its students for the values of Honesty, Regularity and Hard work with a total cash award of Rs 6,000. Three times the award money for Hard work added to that given for honesty amounts to Rs 11,000. The award money given for Honesty and Hard work together is double the one given for Regularity. Represent the above situation algebraically and find the award money for each value, using matrix method. Apart from these values, namely, Honesty, Regularity and Hard work, suggest one more value which the school must include for awards.

If A is a 3 × 3 invertible matrix, then what will be the value of k if det(A^–1) = (det A)^k.

Show that all the diagonal elements of a skew symmetric matrix are zero.

Let find a matrix D such that CD – AB = O.

If the matrix $\mathrm{A} = \left[\begin{array}{ccc}0& \mathrm{a}& -3\\ 2& 0& -1\\ \mathrm{b}& 1& 0\end{array}\right]$ is skew symmertic, find the values of 'a' and 'b'.

Given, $\mathrm{A} = \left[\begin{array}{cc}2& -3\\ -4& 7\end{array}\right]$ compute A^-1 and show that 2A^- = 9I-A