If a, b, and c are real numbers such that c 0 and ac = bc, then a = b. However, if A, B
Chapter 8, Problem 107(choose chapter or problem)
Think About It If a, b, and c are real numbers such that \(c \neq 0\) and ac = bc, then a = b. However, if A, B, and C are nonzero matrices such that AC = BC, then A is not necessarily equal to B. Illustrate this using the following matrices.
\(A=\left[\begin{array}{ll}0&1\\ 0&1\end{array}\right],\quad\ B=\left[\begin{array}{ll}1&0\\ 1&0\end{array}\right],\quad\ C=\left[\begin{array}{ll}2&3\\ 2&3\end{array}\right]\)
Text Transcription:
c neq 0
A = [ _0 1 ^0 1], B = [ _1 0 ^1 0], C = [ _2 3 ^2 3]
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