Express the matrix B = 2 - 2 - 4 - 1 3 4 1 - 2 - 3 as the sum of symmetric and a skew-symmetric matrix.

Given that, B = 2 - 2 - 4 - 1 3 4 1 - 2 - 3 To proof : symmetric and skew symmetric matrix. Let B = P + Q where P = 1 2 B + B ' and Q = 1 2 B - B ' Now, P = 1 2 B + B ' = 1 2 2 - 2 - 4 - 1 3 4 1 - 2 - 3 + 2 - 1 1 - 2 3 - 2 - 4 4 - 3 P = 1 2 B + B ' = 1 2 4 - 3 - 3 - 3 6 2 - 3 2 - 6 P = 1 2 B + B ' = 2 - 3 2 - 3 2 - 3 2 3 1 - 3 2 1 - 3 (symmetric) Q = 1 2 B - B ' = 1 2 2 - 2 - 4 - 1 3 4 1 - 2 - 3 - 2 - 1 1 - 2 3 - 2 - 4 4 - 3 Q = 1 2 B - B ' = 1 2 0 - 1 - 5 1 0 6 5 - 6 0 Q = 1 2 B - B ' = 0 - 1 2 - 5 2 1 2 0 3 5 2 - 3 0 (skew-symmetric) Hence, 2 - 2 - 4 - 1 3 4 1 - 2 - 3 = 2 - 3 2 - 3 2 - 3 2 3 1 - 3 2 1 - 3 + 0 - 1 2 - 5 2 1 2 0 3 5 2 - 3 0 .

If the matrix A = 0 a - 3 2 0 - 1 b 1 0 is skew symmetric, find the values of a and b .

Given that, A = 0 a - 3 2 0 - 1 b 1 0 And the matrix A is given to be skew-symmetric matrix ∴ A T = - A ∴ 0 2 b a 0 1 - 3 - 1 0 = - 0 a - 3 2 0 - 1 b 1 0 ⇒ 0 2 b a 0 1 - 3 - 1 0 = 0 - a 3 - 2 0 1 - b - 1 0 Two matrices A and B are said to be equal if they are of same order and their corresponding elements are equal. Therefore, - a = 2 and b = 3 ⇒ a = - 2 and b = 3 . Hence, the required values are: a = - 2 and b = 3

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Important Questions on Matrices

EASY

Mathematics>Algebra>Matrices>Symmetric and Skew-symmetric Matrices

FInd the number of all possible matrices of order

$3 \times 3$ with each entry $0$ or $1$ .

MEDIUM

Mathematics>Algebra>Matrices>Symmetric and Skew-symmetric Matrices

Express the matrix

B = [\begin{matrix} 2 & - 2 & - 4 \\ - 1 & 3 & 4 \\ 1 & - 2 & - 3 \end{matrix}]

as the sum of symmetric and a skew-symmetric matrix.

EASY

Mathematics>Algebra>Matrices>Symmetric and Skew-symmetric Matrices

A

is a matrix of order

3 \times 2

, and order of the matrix

A^{'}

m \times n

, then

m + n =

_____

EASY

Mathematics>Algebra>Matrices>Symmetric and Skew-symmetric Matrices

A square matrix

A

is said to be skew-symmetric, if

A^{'} =

_____

EASY

Mathematics>Algebra>Matrices>Symmetric and Skew-symmetric Matrices

Which of the following is not required for any of the techniques of DNA fingerprinting available at present?

EASY

Mathematics>Algebra>Matrices>Symmetric and Skew-symmetric Matrices

Expand VNTR and describe its role in DNA fingerprinting.

MEDIUM

Mathematics>Algebra>Matrices>Symmetric and Skew-symmetric Matrices

The number of possible matrices of order

3 \times 3

with each entry

0

1

EASY

Mathematics>Algebra>Matrices>Symmetric and Skew-symmetric Matrices

If the matrix

A = [\begin{matrix} 0 & a & - 3 \\ 2 & 0 & - 1 \\ b & 1 & 0 \end{matrix}]

is skew symmetric, find the values of

a

and

b

EASY

Mathematics>Algebra>Matrices>Symmetric and Skew-symmetric Matrices

f (x) = |\begin{matrix} x^{3} - x & a + x & b + x \\ x - a & x^{2} - x & c + x \\ x - b & x - c & 0 \end{matrix}|

then

EASY

Mathematics>Algebra>Matrices>Symmetric and Skew-symmetric Matrices

A, B

are symmetric matrices of the same order, then

A B - B A

is a

EASY

Mathematics>Algebra>Matrices>Symmetric and Skew-symmetric Matrices

List any two applications of DNA fingerprinting technique.

HARD

Mathematics>Algebra>Matrices>Symmetric and Skew-symmetric Matrices

A number of passengers were severely burnt beyond reorganisation during a train accident. Name and describe the modern technology that can help in handing over the dead to their relative.

EASY

Mathematics>Algebra>Matrices>Symmetric and Skew-symmetric Matrices

DNA fingerprinting is based on;

EASY

Mathematics>Algebra>Matrices>Symmetric and Skew-symmetric Matrices

VNTRs represents-

EASY

Mathematics>Algebra>Matrices>Symmetric and Skew-symmetric Matrices

Basis of DNA fingerprinting lies in;

HARD

Mathematics>Algebra>Matrices>Symmetric and Skew-symmetric Matrices

What is satellite DNA in a genome? Explain their role in DNA fingerprinting.