Let V be a subspace of R^10. Suppose A is a 10times 10 matrix with real entries. Let A^k(V)=A^kx:xin V for kge 1 and A(V)=A^1(V). Which one of the following statements is NOT true?

(D) If dim(V)=dim(A(V))=dim(A^2(V))=cdots=dim(A^5(V)), then dim(A^6(V))=dim(V) necessarily holds

Q14Section A (Section A)14 of 60

Dimensions of successive images

Let $V$ be a subspace of $\mathbb{R}^{10}$ . Suppose $A$ is a $10\times 10$ matrix with real entries. Let $A^k(V)=\{A^k\mathbf{x}:\mathbf{x}\in V\}$ for $k\ge 1$ and $A(V)=A^1(V)$ . Which one of the following statements is NOT true?

Pick an option to check your answer.

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