A total amount of Rs. 7,000 is deposited in three different savings bank accounts with annual interest rates of 5%, 8% and 81/2% respectively. The total annual interest from these three accounts is Rs. 550. Equal amounts have been deposited in 5% and 8% savings accounts. Find the amount deposited in each of the three accounts, with the help of matrices. Write the value.

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 Rs. x each, Rs. y each and Rs. z each for the three respective values to its 3, 2 and 1 students with a total award money of Rs. 1,600. School B wants to spend Rs. 2,300 to award its 4, 1 and 3 students on the respective values (by giving the same award money for the three values as before). If the total amount of awards for one prize on each value is Rs. 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.

Two factories decided to award their employees for three values of
(a) adaptable new techniques,
(b) careful and alert in difficult situations and
(c) keeping calm in tense situations, at the rate of Rs. x, Rs. y and Rs. z per person respectively 2, 4 and 3 employees with a total prize money of Rs. 29,000. The second factory decided to honour respectively 5, 2 and 3 employees with the prize money of Rs. 30,500. If the three prizes per person together cost Rs. 9,500; then
(i) Represent the above situation by a matrix equation and form linear equations using matrix multiplication.
(ii) Solve these equations using matrices
(iii) Which values are reflected in this question?

A school wants to award its students for the value 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.

Find the inverse of the matrix : \(A=\left[ \begin{matrix} a & 0 & 0 \\ 0 & b & 0 \\ 0 & 0 & c \end{matrix} \right] \)
Can you find the inverse for all values of a, b, c? If same rule is applied to the progress of a person, what value is most essential in?