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GATE EE 2019 Set 1 — Question 36

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MCQ+2 / -0.67EasyMatrix AlgebraLinear AlgebraEngineering Mathematics

Engineering Mathematics → Linear Algebra → Matrix Algebra

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Question

Consider a 2×22 \times 2 matrix M=[v1v2]M = [v_1 \quad v_2], where v1v_1 and v2v_2 are the column vectors. Suppose M−1=[u1Tu2T]M^{-1} = \begin{bmatrix} u_1^T \\ u_2^T \end{bmatrix}, where u1Tu_1^T and u2Tu_2^T are the row vectors. Consider the following statements:
Statement 1: u1Tv1=1u_1^T v_1 = 1 and u2Tv2=1u_2^T v_2 = 1
Statement 2: u1Tv2=0u_1^T v_2 = 0 and u2Tv1=0u_2^T v_1 = 0Which of the following options is correct?
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