Explain what is wrong with the following proof attempt. Ide…
Explain what is wrong with the following proof attempt. Identify the two errors. Prove that tr(kA)=ktr(A){“version”:”1.1″,”math”:”tr(kA)=ktr(A)”} for any n×n{“version”:”1.1″,”math”:”n×n”} matrix A and scalar k. Attempt: Let A=a11a12a13a21a22a23a31a32a33{“version”:”1.1″,”math”:”A=a11a12a13a21a22a23a31a32a33″}. Then,trkA=trka11ka12ka13ka21ka22ka23ka31ka32ka33 = ka11+ka22+ka33 = ka11+a22+a33 = ktrA{“version”:”1.1″,”math”:”trkA=trka11ka12ka13ka21ka22ka23ka31ka32ka33 = ka11+ka22+ka33 = ka11+a22+a33 = ktrA”}