Let A = 1 & 0 & 0 \\ 2 & 1 & 0 \\ 3 & 2 & 1 . If u_1 and u_2 are column matrices such that Au_1 = 1 \\ 0 \\ 0 and Au_2 = 0 \\ 1 \\ 0 , then u_1 + u_2 - Mathematics MCQ AIEEE 2012 2026 | ExamTest.live

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Let A = 123012001 . If u_{1} and u_{2} are column matrices such that A u_{1} = 100 and A u_{2} = 010, then u_{1} + u_{2} is equal to:

Solution & Step-by-step Explanation

Let u_{1} = a b c and u_{2} = d e f .From A u_{1} = 100 : a = 1 2 a + b = 0 ⟹ 2 + b = 0 ⟹ b = - 2 3 a + 2 b + c = 0 ⟹ 3 - 4 + c = 0 ⟹ c = 1 So u_{1} = 1 - 2 1 .From A u_{2} = 010 : d = 0 2 d + e = 1 ⟹ e = 1 3 d + 2 e + f = 0 ⟹ 2 + f = 0 ⟹ f = - 2 So u_{2} = 01 - 2 . u_{1} + u_{2} = 1 - 2 1 + 01 - 2 = 1 - 1 - 1 .

Try it yourself before checking the explanation above.

Let A = 123012001 . If u_{1} and u_{2} are column matrices such that A u_{1} = 100 and A u_{2} = 010, then u_{1} + u_{2} is equal to:

- 1 10

- 1 1 - 1

- 1 - 1 0

1 - 1 - 1

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