Question:
Let \(\R\) be the set of real numbers, U be a subspace of \(\R^3\) and M ∈ \(\R^{3×3}\) be the matrix corresponding to the projection on to the subspace U.
Which of the following statements is/are TRUE ?
Let \(\R\) be the set of real numbers, U be a subspace of \(\R^3\) and M ∈ \(\R^{3×3}\) be the matrix corresponding to the projection on to the subspace U.
Which of the following statements is/are TRUE ?
Which of the following statements is/are TRUE ?
Updated On: Jul 9, 2024
- If U is a 1-dimensional subspace of \(\R^3\), then the null space of M is a 1-dimensional subspace.
- If U is a 2-dimensional subspace of \(\R^3\), then the null space of M is a 1-dimensional subspace.
- M2 = M
- M3 = M
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The Correct Option is B, C, D
Solution and Explanation
The correct option is (B) : If U is a 2-dimensional subspace of \(\R^3\), then the null space of M is a 1-dimensional subspace, (C) : M2 = M and (D) : M3 = M.
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