Problem 4: (7 points) Let T: R₂[z] → R₂[z] be a given linear operator defined by T(ao+ar+a22²) = ₂x². Find the kernel of

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Problem 4 7 Points Let T R Z R Z Be A Given Linear Operator Defined By T Ao Ar A22 X Find The Kernel Of 1 (28.28 KiB) Viewed 24 times

Problem 4: (7 points) Let T: R₂[z] → R₂[z] be a given linear operator defined by T(ao+ar+a22²) = ₂x². Find the kernel of T. A) < (0,1,0) > (B) <1,r> C) <1,2² > D) <1,1²> E) <1,1,²> Problem 5: (7 points) Find the determinant of the matrix A) 0 B) a C) a(b-a)(b-c) D) a(c-a) (c-b) E a(b-a) (c-b) a a a abb a b C Problem 6: (7 points) Given A, B,C Mnxn(R), which one of the following statements is false: A) If A is an eigenvalue of A with associated eigenvectore then u is an eigenvector of 4², associated with the eigenvalue X². B) The determinant of ABC is |A|B|C|. C) M₁ M₂ is orthogonal if M₁ and M₂ are both orthogonal matrices. D The determinant of In + A is 1+ det 4. E) det A# 0 if and only if A is invertible.