In the matrix ,write: (i) The order of the matrix (ii) The number of elements, (iii) Write the elements a₁₃, a₂₁, a₃₃, a₂₄, a₂₃

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

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

Construct a 3 × 4 matrix, whose elements are given by (i)(ii)

Find the value of x, y, and z from the followingequation: (i) (ii) (iii)

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

is a square matrix, if (I) m n (III) m = n (IV) None of these

Which of the given values of x and y make the following pair of matrices equal (A) (B) Not possible to find (C) (D)

The number of all possible matrices of order 3 × 3 with each entry 0 or 1 is: (I) 27 (II) 18 (III) 81(D) 512

Let Find each of thefollowing (i) (ii) (iii) (iv) (v)

Compute the following: (i)(ii) (iii) (v)

Compute the indicatedproducts (i) (ii) (iii) (iv) (v) (I)

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

If and then compute .

Simplify

Find X and Y, if (i) and (ii) and

Find X, if and

Find x and y, if

Solve the equation for x, y, z and t if

If , find values of x and y.

Given , find the values of x, y, zand w.

If , show that .

Show that (i) (ii)

Findif

If, provethat

If and , find k so that

Ifand I is the identity matrix of order 2, showthat

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

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.

Assume X, Y, Z, W and P are matricesof order, and respectively. The restriction on n, k and psothatwill be definedare: (I) k = 3, p =n (II) k is arbitrary, p =2 (III) p is arbitrary, k =3 D. k = 2, p = 3

Assume X, Y, Z, W and P are matricesof order, and respectively. If n = p, then the order ofthematrixis A p × 2 B 2 × n C n × 3 D p × n

Find the transpose of each of the following matrices: (i)(ii)(iii)

If and , then verify that (i) (ii)

Ifand , then verify that (i) (ii)

If and , then find

For the matrices A and B, verify that (AB)' =where (i) (ii)

If (i) , then verifythat (ii) , then verifythat

(I) Show thatthematrixis a symmetricmatrix (II) Show that the matrix is a skew symmetric matrix

For the matrix , verifythat (I) is a symmetricmatrix (II) is a skew symmetric matrix

Find and , when

Express the following matrices as the sum of a symmetric and a skew symmetric matrix: (i) (ii) (I) (II)

If A, B are symmetric matrices of same order, then AB - BA is a A. Skew symmetric matrix B. Symmetric matrixC. Zero matrix D. Identity matrix

If,then, if the value of ais A.B. C. pD.

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.

Matrices A and B will be inverse of each other only if A. AB = BA C. AB = 0, BA = I B. AB = BA =0 D. AB = BA =I

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

If, provethat

If , then prove where n is any positive integer

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

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

Solve system of linear equations, using matrix method.

For whatvaluesof?

If , showthat

Find x, if

A manufacturer produces three products x, y, z which he sells in two markets. Annual sales are indicated below: Market Products I 10000 2000 18000 II 6000 20000 8000 (I) 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 matrixalgebra. (II) If the unit costs of the above three commodities are Rs 2.00, Rs 1.00 and 50 paise respectively. Find the grossprofit.

Find the matrix X so that

If A and B are square matrices of the same order such that AB = BA, then prove by inductionthat. Further,provethatfor all n ?N

Choose the correct answer in the following questions: If issuch thatthen A. B. C. D.

If the matrix A is both symmetric and skew symmetric, then (I) A is a diagonalmatrix (II) A is a zeromatrix (III) A is a squarematrix (IV) None of these

If A is square matrixsuchthatthenis equal to A. A B. I - A C. I D. 3A