3.4.14) By Theorem 3.12, A(adj(A)) = det(A)I n. Both
... 3.4.14) By Theorem 3.12, A(adj(A)) = det(A)In . Both sides are n × n matrices, so we can take the determinant of both to get det(A(adj(A))) = det(det(A)In ). The right hand side of this is a scalar matrix with det(A) in each of the n entries on the diagonal. Thus, its determinant is (det(A))n . We c ...
... 3.4.14) By Theorem 3.12, A(adj(A)) = det(A)In . Both sides are n × n matrices, so we can take the determinant of both to get det(A(adj(A))) = det(det(A)In ). The right hand side of this is a scalar matrix with det(A) in each of the n entries on the diagonal. Thus, its determinant is (det(A))n . We c ...
4.4 Matrices: Basic Operations
... and a Column Matrix In order to understand the general procedure of matrix multiplication, we will introduce the concept of the product of a row matrix by a column matrix. A row matrix consists of a single row of numbers, while a column matrix consists of a single column of numbers. If the numbe ...
... and a Column Matrix In order to understand the general procedure of matrix multiplication, we will introduce the concept of the product of a row matrix by a column matrix. A row matrix consists of a single row of numbers, while a column matrix consists of a single column of numbers. If the numbe ...
Chapter A.1. Basic Algebra
... (6). On the other hand, the answer as to whether Zn satisfies (7) or the weaker (70 ) and (700 ) depends upon the particular value of the modulus n. For instance, all are true when n = 2. For n = 6 we have 2 · 3 = 0 (mod 6) (whence 2 · 3 = 2 · 0 (mod 6)); yet neither 2 nor 3 equals 0 in the integers ...
... (6). On the other hand, the answer as to whether Zn satisfies (7) or the weaker (70 ) and (700 ) depends upon the particular value of the modulus n. For instance, all are true when n = 2. For n = 6 we have 2 · 3 = 0 (mod 6) (whence 2 · 3 = 2 · 0 (mod 6)); yet neither 2 nor 3 equals 0 in the integers ...
Notes 4.4 - TeacherWeb
... Product of a Row Matrix and a Column Matrix In order to understand the general procedure of matrix multiplication, we will introduce the concept of the product of a row matrix by a column matrix. A row matrix consists of a single row of numbers, while a column matrix consists of a single column ...
... Product of a Row Matrix and a Column Matrix In order to understand the general procedure of matrix multiplication, we will introduce the concept of the product of a row matrix by a column matrix. A row matrix consists of a single row of numbers, while a column matrix consists of a single column ...
