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TRUE OR FALSE NO EXPLANATION NEEDED JUST WRITE TRUE OR FALSE 1- If A and B are m x n, then both ABT and ATB are defined. () 2- If A is an m x n matrix and the equation Ax= b is consistent for every b in Rm, then A has m pivot columns. ( ) 3- Left-multiplying a matrix B by a diagonal matrix A, with nonzero entries on the diagonal, scales the rows of B. ()

TRUE OR FALSE NO EXPLANATION NEEDED JUST WRITE TRUE OR FALSE 1- If A and B are m x n, then both ABT and ATB are defined. () 2- If A is an m x n matrix and the equation Ax= b is consistent for every b in Rm, then A has m pivot columns. ( ) 3- Left-multiplying a matrix B by a diagonal matrix A, with nonzero entries on the diagonal, scales the rows of B. ()

College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter6: Linear Systems
Section6.3: Matrix Algebra
Problem 85E: Determine if the statement is true or false. If the statement is false, then correct it and make it...
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TRUE OR FALSE NO EXPLANATION NEEDED JUST WRITE TRUE OR FALSE 1- If A and B are m x n, then both ABT and ATB are defined. () 2- If A is an m x n matrix and the equation Ax= b is consistent for every b in Rm, then A has m pivot columns. () 3- Left-multiplying a matrix B by a diagonal matrix A, with nonzero entries on the diagonal, scales the rows of B. () 4- If a system Ax= 0 has more than one solution, then so does the system Ax= b. () 5- If two rows of a 3x3 matrix A are the same, then det A = 0. () 6- If AB = 1, then A is invertible. ()
Transcribed Image Text:TRUE OR FALSE NO EXPLANATION NEEDED JUST WRITE TRUE OR FALSE 1- If A and B are m x n, then both ABT and ATB are defined. () 2- If A is an m x n matrix and the equation Ax= b is consistent for every b in Rm, then A has m pivot columns. () 3- Left-multiplying a matrix B by a diagonal matrix A, with nonzero entries on the diagonal, scales the rows of B. () 4- If a system Ax= 0 has more than one solution, then so does the system Ax= b. () 5- If two rows of a 3x3 matrix A are the same, then det A = 0. () 6- If AB = 1, then A is invertible. ()
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