Question

Which of the following statements is/are TRUE ?
Note: $\R$ denotes the set of real numbers.

• A. 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.
• 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.
• C. 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.
• 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.

Answer 1

Answer: (B), (D)

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.

Answer 2

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.