Math Answers

Give example, with justification , of the following: (1) two non -zero ,3×3 matrices A and B , with|A| =0, |B|= (5/7)i ; (2) . two non - singular 2×2 matrices C and D , with |C| = √2 |D| ?

Apply the Gaussian elimination process to determine values of lembda for which the following linear system is consistent: x- 3y+4 =0 , 3x-2y=lembda , y= 6- 2x .?

The annual bonus given to the employees of a company is 5 % of their taxable income, after the state and central taxes are deducted. The state tax is 10% of taxable income. The central tax is 20% of taxable income after deducting the state tax . Formulate this situation for determining the bonus, as a linear system?

Solve x^4 -8x^3+21x^2- 20 x +5=0 given that the sum of two of its roots is 4

Find the roots of the equation 2x^3 - x^2 -22 x -24 = 0 , if two of them are in the ratio 3: 4 ?

Find the polynomial over R of least degree which has i-3 and √7 +5i as its roots

Find the sum of 5th roots of unity?

Apply De Moivre's theorem to write (√3+i) ^5 in the form a+ib , with a, b belongs to R ?

Obtain the polar and exponential representations of z_1 , z_2 and z_1 z_2 , where z_1. = 1/2 - ( 2i) and z_2 = 3+i ?

Express z= 1/(-5-i) in standard (algebraic) form. Further, give an Argand diagram in which z , bar z and -z are plotted?