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Are the following statements true or false? ? 1. If A is a matrix, then the dimension of the row space of A is equal to the dimension of the column space of A. ? 2. If A and B are equivalent matrices, then col(A) = col(B). ? 3. If A and B are equivalent matrices, then row(A) = row( B). ? 4. If A is a 8 x 5 matrix, and T(x) = Ax is a linear transformation, then I can be one-to-one.

Are the following statements true or false? ? 1. If A is a matrix, then the dimension of the row space of A is equal to the dimension of the column space of A. ? 2. If A and B are equivalent matrices, then col(A) = col(B). ? 3. If A and B are equivalent matrices, then row(A) = row( B). ? 4. If A is a 8 x 5 matrix, and T(x) = Ax is a linear transformation, then I can be one-to-one.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Are the following statements true or false? 1. If A is a matrix, then the dimension of the row space of A is equal to the dimension of the column space of A. 2. If A and B are equivalent matrices, then col(A) = col( B). 3. If A and B are equivalent matrices, then row(A) = row( B). 4. If A is a 8 x5 matrix, and T(x) = Ax is a linear transformation, then T can be one-to-one.
Transcribed Image Text:Are the following statements true or false? 1. If A is a matrix, then the dimension of the row space of A is equal to the dimension of the column space of A. 2. If A and B are equivalent matrices, then col(A) = col( B). 3. If A and B are equivalent matrices, then row(A) = row( B). 4. If A is a 8 x5 matrix, and T(x) = Ax is a linear transformation, then T can be one-to-one.
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