Consider the system of equations x + 2y - z = a, x + y + 3z = b, 2x + 3y + 2z = c. Consider the following statements: (I) For every (a, b, c) in R^3, the above system has a solution. (II) For (a, b, c) = (0, 0, 0), the solution set is given by (-7t, 4t, t) : t in R. Which of the following statements is correct?

(B) Only statement (II) is correct

Q39Section ST (Statistics (Q11–Q65))39 of 65

Singular 3x3 system

Consider the system of equations $x + 2y - z = a$ , $x + y + 3z = b$ , $2x + 3y + 2z = c$ . Consider the following statements: (I) For every $(a, b, c) \in \mathbb{R}^3$ , the above system has a solution. (II) For $(a, b, c) = (0, 0, 0)$ , the solution set is given by $\{(-7t, 4t, t) : t \in \mathbb{R}\}$ . Which of the following statements is correct?

Pick an option to check your answer. In a mock test a wrong answer here costs 2/3 mark.

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