Lecture 2 : Operations on matrices: addition & Multiplication of matrices

Assume X, Y, Z, Wand P are matrices of order, and respectively. If n= p, then the order of the matrix is

A) p ×2

B) 2 × n

C) n ×3

D) p × n

Assume X, Y, Z, W and P are matrices of order, and respectively. The restriction on n, k and p so that will be defined are:

A) k = 3, p = n

B) k is arbitrary, p = 2

C) p is arbitrary, k = 3

D) k = 2, p = 3

The bookshop of a particular school has 10 dozen chemistry books, 8 dozen physics books, 10 dozen economics books. Their selling prices are Rs 80, Rs 60 and Rs 40 each respectively. Find the total amount the bookshop will receive from selling all the books using matrix algebra.

A trust fund has Rs 30,000 that must be invested in two different types of bonds. The first bond pays 5% interest per year, and the second bond pays 7% interest per year. Using matrix multiplication, determine how to divide Rs 30,000 among the two types of bonds. If the trust fund must obtain an annual total interest of:

(a) Rs 1,800 (b) Rs 2,000

Ifand I is the identity matrix of order 2, show that 

If and, find k so that 

If, prove that 

Find if

Show that

(i) 

(ii) 

If, show that

Given, find the values of x, y, zand

w.

If, find values of xand y.

Solve the equation for x, y, zand t if

Find xand y, if

Find X, if and 

Find X and Y, if

(i) and

(ii) and

Simplify 

If andthen compute.

If, and, then compute and. Also, verify that

Compute the indicated products

(i) 

(ii) 

(iii) 

(iv) 

(v) 

(vi) 

Compute the following:

(i)  (ii) 

(iii) 

(v) 

Let 

Find each of the following

(i)  (ii)  (iii) 

(iv)  (v)