) is (a) ∆ ∆ ∆ ∆ (b) ∆ ∆ ∆ ∆ (c) ∆ ∆ ∆ ∆ (d) −∆ ∆ −∆ ∆ . If A adjA n n and then the value n is (a) (b) (c) (d) . Rank of a null matrix is (a) (b) – (c) ∞ (d) Miscellaneous problems . Find the rank of the matrix A = .
Find the rank of the matrix A = . Find the rank of the matrix A = . Examine the consistency of the system of equations: . Find k if the equations k are consistent.
. Find k if the equations x = , k are inconsistent. . Solve the equations , = − by using Cramer’s rule.
. The cost of 2kg. of wheat and 1kg. of sugar is ` .
The cost of 1kg. of wheat and 1kg. of rice is ` . The cost of 3kg.
of wheat, 2kg. of sugar and 1kg of rice is ` . Find the cost of each per kg., using Cramer’s rule. .
A salesman has the following record of sales during three months for three items A, B and C, which have different rates of commission. Months Sales of units Total commission drawn (in ` ) January February March XII Std - Business Maths & Stat EM Chapter - - Applications of Matrices and Determinants Find out the rate of commission on the items A, B and C by using Cramer’s rule. . The subscription department of a magazine sends out a letter to a large mailing list inviting subscriptions for the magazine.
Some of the people receiving this letter already subscribe to the magazine while others do not. From this mailing list, % of those who already subscribe will subscribe again while % of those who do not now subscribe will subscribe. On the last letter it was found that % of those receiving it ordered a subscription. What percent of those receiving the current letter can be expected to order a subscription?
Summary In this chapter we have acquired the knowledge of: Rank of a matrix The rank of a matrix A is the order of the largest non-zero minor of A The rank of a matrix A is the order of the largest non-zero minor of A r ( ) A ≥ If A is a matrix of order m , then r ( ) A £ minimum of m n