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Let 7, j, k be the versors of the coordinate axis of R3. Let ✓ = -j+ k Let us denote by X the vector product. Let f: R³ R³ be the endomorphism defined as f(u) = (vx ū) + 2ū, for each ū € R³. Which one of the following statements is true? © (a)t(t² + t-3) is the characteristic polynomial of f. (b) f is injective but not surjective. (c) f is surjective but not injective. (d) f is injective.

Let 7, j, k be the versors of the coordinate axis of R3. Let ✓ = -j+ k Let us denote by X the vector product. Let f: R³ R³ be the endomorphism defined as f(u) = (vx ū) + 2ū, for each ū € R³. Which one of the following statements is true? © (a)t(t² + t-3) is the characteristic polynomial of f. (b) f is injective but not surjective. (c) f is surjective but not injective. (d) f is injective.

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Let i, j, k be the versors of the coordinate axis of Let us denote by X the vector product. Let f: R³ f(u) = (vx ū) + 2ū, for each ū € R³. Which one of the following statements is true? 3. Let ✓ = -j+ k R³ be the endomorphism defined as © (a)t(t² + t − 3) is the characteristic polynomial of f. (b) f is injective but not surjective. (c) f is surjective but not injective. (d) f is injective.
Transcribed Image Text:Let i, j, k be the versors of the coordinate axis of Let us denote by X the vector product. Let f: R³ f(u) = (vx ū) + 2ū, for each ū € R³. Which one of the following statements is true? 3. Let ✓ = -j+ k R³ be the endomorphism defined as © (a)t(t² + t − 3) is the characteristic polynomial of f. (b) f is injective but not surjective. (c) f is surjective but not injective. (d) f is injective.
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