Solved GATE DA 2024 Question Paper | DETAILED VIDEO SOLUTIONS | DA & AI | Q. 48
Q.48 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 ∈ ℝ
3
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 ∈ ℝ
3
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.
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