Question

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ii)A square matrix A is said to be singular matrix If ......
a) A=A b) |A| = 0 c) A 70 d) A A
i)Find area of the circle centre at (1,2) and passing through (4,6)
ii)Define Scalar matrix
iii) Write down the sets in set builder form {10,20,30,40,50)​

Answer 1

Step-by-step explanation:

ii) A square matrix is singular if and only if its determinant is 0.

ii) A square matrix, in which all diagonal elements are equal to same scalar and all other elements are zero, is called a scalar matrix.

Or

A diagonal matrix, in which all diagonal elements are equal to same scalar, is called a scalar matrix.

iii) {x:x is a multiple of 10 and less then 6}

Answer 2

ii) a SQUARE matrix is said to be singular if its determinant is equal to ZERO.

   i.e |A| = 0

correct answer is option 'b'

i) Area of a circle is

$A= \pi * r^2$

Radius of the circle having center and passing through a point is given by

$(x_c-x)^2 +(y_c-y)^2 = r^2$

by substituting the center coordinates and point coordinates in the above equation

$(1-4)^2+(2-6)^2=r^2\\(-3)^2+(-4)^2=r^2\\r=5$

Then, area of the given circle is $A = \pi * 5^2 = 78.54 sq.units$

ii) A scalar matrix is the SQUARE matrix whose diagonal elements are some CONSTANT and the remaining are ZEROS

                                           $\left[\begin{array}{ccc}K&0&0\\0&K&0\\0&0&K\end{array}\right]$

iii) given set is {10,20,30,40,50}

$10 =1 *10\\20 = 2*10\\30 =3*10\\40 =4*10\\50= 5*10$

{x: x= n*10, n∈ N and 1≤n≤5}

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