Apply the Gaussian elimination process to determine values of λ for which the following linear system is consistent:
x − 3y + 4 = 0, 3x − 2y = λ, y = 6 − 2x .
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Is Cramer’s Rule applicable for solving the linear system below? If yes, apply it.
Otherwise, alter the last equation in the system so that the solution can be obtained
by applying the Rule.
x + y + z = π
− πx + πy +sqrt(2z) = 0
π2 x + π2 y + 2z = 0 .
The annual bonus given to the employees of a company is 5% of their taxable incomes, 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.
Express z = 1/-5 − i in standard (algebraic) form. Further, give an Argand diagram in which z, –z and − z are plotted.
Apply the Gaussian elimination process to determine values of λ for which the following linear system is consistent:
x − 3y + 4 = 0, 3x − 2y = λ, y = 6 − 2x .
Prove that 
Find the sum of the 5th roots of unity.
Obtain the polar and exponential representations of z1 , z2 and z1z 2 , where zi = 1/2 - 2i and z2 = 3 + i