Question:
Which of the following statements is/are TRUE ?
Note: \(\R\) denotes the set of real numbers.
Which of the following statements is/are TRUE ?
Note: \(\R\) denotes the set of real numbers.
Note: \(\R\) denotes the set of real numbers.
Updated On: Jul 9, 2024
- There exist M ∈ \(\R^{3×3}\), p ∈ \(\R^3\), and q E R3 such that Mx = p has a unique solution and Mx = q has infinite solutions.
- There exist M ∈ \(\R^{3×3}\), p ∈ \(\R^3\), and q E R3 such that Mx = p has no solutions and Mx = q has infinite solutions.
- There exist M ∈ \(\R^{2×3}\), p ∈ \(\R^2\), and q ∈ \(\R^2\) such that Mx = p has a unique solution and Mx = q has infinite solutions.
- There exist M ∈ \(\R^{3×2}\), p ∈ \(\R^3\), and q ∈ \(\R^3\) such that Mx = p has a unique solution and Mx = q has no solutions.
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The Correct Option is B, D
Solution and Explanation
The correct option is (B) : There exist M ∈ \(\R^{3×3}\), p ∈ \(\R^3\), and q E R3 such that Mx = p has no solutions and Mx = q has infinite solutions and (D) : There exist M ∈ \(\R^{3×2}\), p ∈ \(\R^3\), and q ∈ \(\R^3\) such that Mx = p has a unique solution and Mx = q has no solutions.
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