Let
by
a. Assume that
b. Write out the distinct elements of
c. Let
Consider the matrices
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ELEMENTS OF MODERN ALGEBRA
- 15. Repeat Exercise with, the multiplicative group of matrices in Exercise of Section. 14. Let be the multiplicative group of matrices in Exercise of Section, let under multiplication, and define by a. Assume that is an epimorphism, and find the elements of. b. Write out the distinct elements of. c. Let be the isomorphism described in the proof of Theorem, and write out the values of.arrow_forward38. Let be the set of all matrices in that have the form with all three numbers , , and nonzero. Prove or disprove that is a group with respect to multiplication.arrow_forwardSuppose that A is an invertible matrix over and O is a zero matrix. Prove that if AX=O, then X=O.arrow_forward
- 44. Consider the set of all matrices of the form, where and are real numbers, with the same rules for addition and multiplication as in. a. Show that is a ring that does not have a unity. b. Show that is not a commutative ring.arrow_forwardProve that if A is similar to B and A is diagonalizable, then B is diagonalizable.arrow_forward
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