Solutions to Homework Set 6
... 1) A group is simple if it has no nontrivial proper normal subgroups. Let G be a simple group of order 168. How many elements of order 7 are there in G? Solution: Observe that 168 = 23 · 3 · 7. Every element of order 7 generates a cyclic group of order 7 so let us count the number of such subgroups: ...
... 1) A group is simple if it has no nontrivial proper normal subgroups. Let G be a simple group of order 168. How many elements of order 7 are there in G? Solution: Observe that 168 = 23 · 3 · 7. Every element of order 7 generates a cyclic group of order 7 so let us count the number of such subgroups: ...
Section 9.5: The Algebra of Matrices
... 6. The product of an (m n) matrix A and an (n k) matrix B is an (m k) matrix whose elements are formed by taking the inner product of each row of A with each column of B. 7. Properties of matrix arithmetic: a. A+ (B + C) = (A + B) + C (associative property of addition) b. A(BC) = (AB)C (associ ...
... 6. The product of an (m n) matrix A and an (n k) matrix B is an (m k) matrix whose elements are formed by taking the inner product of each row of A with each column of B. 7. Properties of matrix arithmetic: a. A+ (B + C) = (A + B) + C (associative property of addition) b. A(BC) = (AB)C (associ ...
Your Title Here - World of Teaching
... numbers in rows and columns. The ORDER of a matrix is the number of the rows and columns. The ENTRIES are the numbers in the matrix. ...
... numbers in rows and columns. The ORDER of a matrix is the number of the rows and columns. The ENTRIES are the numbers in the matrix. ...
Document
... If a matrix A is reflected by T1 then magnified by T2 to give matrix B then the single transformation that would transform A into B is T 2T1 (in that order). H Jackson 2010 / Academic Skills ...
... If a matrix A is reflected by T1 then magnified by T2 to give matrix B then the single transformation that would transform A into B is T 2T1 (in that order). H Jackson 2010 / Academic Skills ...
Problems:
... If A, B M n ( F ) where A ~ B (specially, A = S-1BS, where det S 0 ), then the following properties hold: (i) det A = det B; (ii) if A is diagonalizable, then so is B; (iii) if x is an eigenvector of A, then Sx is an eigenvector of B. If A, B M n ( F ) are simultaneously diagonalizable, th ...
... If A, B M n ( F ) where A ~ B (specially, A = S-1BS, where det S 0 ), then the following properties hold: (i) det A = det B; (ii) if A is diagonalizable, then so is B; (iii) if x is an eigenvector of A, then Sx is an eigenvector of B. If A, B M n ( F ) are simultaneously diagonalizable, th ...
