consider the system of equations px+qy=0 rx+sy=0 where p,q,r,s∈0 and 1 only. find the probability that the system of equations has a unique solution.

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Q. Consider the system of equations

a x +

= 0, c x + d y = 0

, where

a, b, c, d \in {0, 1}

.

STATEMENT--1: The probability that the system of equations has a unique solution is

3 / 8

STATEMENT-2: The probability that the system of equations has a solution is

1

Q. Assertion :Consider the system of equations

a x + b y = 0, c x + d y = 0;

where

a, b, c, d ϵ {0, 1} .

STATEMENT-1: The probability that the system of equations has a unique solution is

\frac{3}{8},

and

Reason: STATEMENT-2: The probability that the system of equations has a solution is 1.

Consider the system of equations ax + by = 0, cx + dy = 0 where a, b, c, d $ε$ {0, 1}. The probability that the system of equations has unique solution is

Q. If

p \neq a, q \neq b, r \neq c

and the system of equations

p x + a y + a z = 0

b x + q y + b z = 0

c x + c y + r z = 0

has a non-trivial solution , then the value of

\frac{p}{p - a} + \frac{q}{q - b} + \frac{r}{r - c}

Q. Let the homogeneous system of linear equations

p x + y + z = 0, x + q y + z = 0

, and

x + y + r z = 0

, where

p, q, r \neq 1,

have a non-zero solution, then the value of

\frac{1}{1 - p} + \frac{1}{1 - q} + \frac{1}{1 - r}

is.

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