Chapter-3. 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

 If A is square matrix such that then is equal to

A. A B. I - A C. I D. 3A

If the matrix Ais both symmetric and skew symmetric, then

A. A is a diagonal matrix

B. A is a zero matrix

C. A is a square matrix

D. None of these

Choose the correct answer in the following questions:

If is such that then

If Aand B are square matrices of the same order such that AB= BA, then prove by induction that. Further, prove that for all n ∈ N

Find the matrix X so that 

A manufacturer produces three products x, y, z which he sells in two markets.

Annual sales are indicated below:

(a) If unit sale prices of x, y and z are Rs 2.50, Rs 1.50 and Rs 1.00, respectively, find the total revenue in each market with the help of matrix algebra.

(b) If the unit costs of the above three commodities are Rs 2.00, Rs 1.00 and 50 paise respectively. Find the gross profit.

Find x, if 

If, show that 

For what values of?

Find the values of x, y, z if the matrix satisfy the equation 

Show that the matrix is symmetric or skew symmetric according as A is symmetric or skew symmetric.

If A and B are symmetric matrices, prove that AB- BA is a skew symmetric matrix.

If, then prove where n is any positive integer

If, prove that 

Let, show that, where I is the identity matrix of order 2 and n ∈ N

Matrices A and Bwill be inverse of each other only if

A. AB= BA

C. AB= 0, BA = I

B. AB= BA = 0

D. AB= BA = I

Find the inverse of each of the matrices, if it exists.

Find the inverse of each of the matrices, if it exists.

Find the inverse of each of the matrices, if it exists.

Find the inverse of each of the matrices, if it exists.

Find the inverse of each of the matrices, if it exists.

Find the inverse of each of the matrices, if it exists.

Find the inverse of each of the matrices, if it exists.

Find the inverse of each of the matrices, if it exists.

Find the inverse of each of the matrices, if it exists.

Find the inverse of each of the matrices, if it exists.

Find the inverse of each of the matrices, if it exists.

Find the inverse of each of the matrices, if it exists.

Find the inverse of each of the matrices, if it exists.

Find the inverse of each of the matrices, if it exists.

Find the inverse of each of the matrices, if it exists.

Find the inverse of each of the matrices, if it exists.

If, then, if the value of α is

A.  B. 

C. π D. 

If A, Bare symmetric matrices of same order, then AB- BAis a

A. Skew symmetric matrix B. Symmetric matrix

C. Zero matrix D. Identity matrix

Express the following matrices as the sum of a symmetric and a skew symmetric matrix:

(i) 

(ii) 

(iii) 

(iv) 

Find and, when 

For the matrix, verify that

(i)  is a symmetric matrix

(ii)  is a skew symmetric matrix

(i) Show that the matrix is a symmetric matrix

(ii) Show that the matrix is a skew symmetric matrix

If (i) , then verify that 

(ii) , then verify that 

For the matrices Aand B, verify that (AB)“² =  where

(i) 

(ii) 

If and, then find 

If and, then verify that

(i) 

(ii) 

If and, then verify that

(i) 

(ii) 

Find the transpose of each of the following matrices:

(i)  (ii)  (iii) 

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) 

The number of all possible matrices of order 3 x 3 with each entry 0 or 1 is:

(A) 27

(B) 18

(C) 81

(D) 512

is a square matrix, if

(A) m < n

(B) m> n

(C) m= n

(D) None of these

Find the value of a, b, c, and d from the equation:

Find the value of x, y, and zfrom the following equation:

(i)  (ii) 

(iii) 

onstruct a 3 ×4 matrix, whose elements are given by

(i)  (ii) 

Construct a 2 ×2 matrix,, whose elements are given by:

If a matrix has 18 elements, what are the possible orders it can have? What, if it has 5 elements?

If a matrix has 24 elements, what are the possible order it can have? What, if it has 13 elements?

In the matrix, write:

(i) The order of the matrix (ii) The number of elements,

(iii) Write the elements a₁₃, a₂₁, a₃₃, a₂₄, a₂₃