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I. True of False Choose True if the statement is correct, otherwise False. 1. Matrices are often represented by single small letters a, b, c... etc. 2. Two m x n matrices A and B are equal if aj=bij for each i & j. (i.e., the two matrices have same size, and all the corresponding elements are equal). 3. Matrices A & B are said to be conformable in the order AB if, and only if, the number of rows in A is equal to the number of columns in B. 4. Suppose Matrix A is having 4 rows and 3 columns, and Matrix B is having 3 rows and 2 columns. The product size of AB is a 4 x 2 matrix. 5. Suppose B is the matrix obtained from an n x n matrix A by multiplying the entries in a row/column by a non-zero constant and adding the result to the corresponding entries in another row/column. Then, det(B) = det(A). 6. Cramer's rule is not applicable if the system is homogeneous. 7. Integer Powers of a complex number can also be obtained by multiplying a complex number in rectangular form by itself n times.

I. True of False Choose True if the statement is correct, otherwise False. 1. Matrices are often represented by single small letters a, b, c... etc. 2. Two m x n matrices A and B are equal if aj=bij for each i & j. (i.e., the two matrices have same size, and all the corresponding elements are equal). 3. Matrices A & B are said to be conformable in the order AB if, and only if, the number of rows in A is equal to the number of columns in B. 4. Suppose Matrix A is having 4 rows and 3 columns, and Matrix B is having 3 rows and 2 columns. The product size of AB is a 4 x 2 matrix. 5. Suppose B is the matrix obtained from an n x n matrix A by multiplying the entries in a row/column by a non-zero constant and adding the result to the corresponding entries in another row/column. Then, det(B) = det(A). 6. Cramer's rule is not applicable if the system is homogeneous. 7. Integer Powers of a complex number can also be obtained by multiplying a complex number in rectangular form by itself n times.

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter2: The Integers
Section2.2: Mathematical Induction
Problem 29E
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I. True of False Choose True if the statement is correct, otherwise False. 1. Matrices are often represented by single small letters a, b, c... etc. 2. Two m x n matrices A and B are equal if aj=bij for each i & j. (i.e., the two matrices have same size, and all the corresponding elements are equal). 3. Matrices A & B are said to be conformable in the order AB if, and only if, the number of rows in A is equal to the number of columns in B. 4. Suppose Matrix A is having 4 rows and 3 columns, and Matrix B is having 3 rows and 2 columns. The product size of AB is a 4 x 2 matrix. 5. Suppose B is the matrix obtained from an n x n matrix A by multiplying the entries in a row/column by a non-zero constant and adding the result to the corresponding entries in another row/column. Then, det(B) = det(A). 6. Cramer's rule is not applicable if the system is homogeneous. 7. Integer Powers of a complex number can also be obtained by multiplying a complex number in rectangular form by itself n times.
Transcribed Image Text:I. True of False Choose True if the statement is correct, otherwise False. 1. Matrices are often represented by single small letters a, b, c... etc. 2. Two m x n matrices A and B are equal if aj=bij for each i & j. (i.e., the two matrices have same size, and all the corresponding elements are equal). 3. Matrices A & B are said to be conformable in the order AB if, and only if, the number of rows in A is equal to the number of columns in B. 4. Suppose Matrix A is having 4 rows and 3 columns, and Matrix B is having 3 rows and 2 columns. The product size of AB is a 4 x 2 matrix. 5. Suppose B is the matrix obtained from an n x n matrix A by multiplying the entries in a row/column by a non-zero constant and adding the result to the corresponding entries in another row/column. Then, det(B) = det(A). 6. Cramer's rule is not applicable if the system is homogeneous. 7. Integer Powers of a complex number can also be obtained by multiplying a complex number in rectangular form by itself n times.
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