Determine whether the following statements are always true or sometimes false. Circle T for true, F for false. You DO NOT need to justify your answers. Let A, B, and C be n x n matrices. (a) T F (A+B)² = A² + 2AB+ B². (b) Т F If rref(A) has a row of zeros, then the linear system Ax = 0 has non-trivial solution. (c) T F (AB)" = AT B". (d) T F A linear system with 3 equations and 3 unknowns is consistent. (е) Т F If A and B are nonsingular, then AB is nonsingular.
Determine whether the following statements are always true or sometimes false. Circle T for true, F for false. You DO NOT need to justify your answers. Let A, B, and C be n x n matrices. (a) T F (A+B)² = A² + 2AB+ B². (b) Т F If rref(A) has a row of zeros, then the linear system Ax = 0 has non-trivial solution. (c) T F (AB)" = AT B". (d) T F A linear system with 3 equations and 3 unknowns is consistent. (е) Т F If A and B are nonsingular, then AB is nonsingular.
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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Transcribed Image Text:Determine whether the following statements are always true or sometimes false.
Circle T for true, F for false. You DO NOT need to justify your answers.
Let A, B, and C be n x n matrices.
(а) Т F (A+ B)? — А? + 2АВ + B?.
(b) Т F
If rref(A) has a row of zeros, then the linear system Ax = 0
has non-trivial solution.
(c) T
F (АB)T — АТВТ.
(d) T
F
A linear system with 3 equations and 3 unknowns is consistent.
(е) Т F
If A and B are nonsingular, then AB is nonsingular.
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