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.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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TRUE OR FALSE (please answer all, will upvote immediately)

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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