a11 a12 a13 b11 b12 b13 Let A a21 a22 a23 | and B b21 b22 b23 be given. Which of the following statement or a31 a32 a33 b31 b32 b33 statements are absolutely correct? I. If AB = 0, then A = 0 or B = 0. II. (A+B)² = A²+2AB + B² dir. a11 a12 a13 III. For k e R, kA = | ka21 ka ka23 a31 a32 a 33 IV. For k + 0, if A-1 exists, then (kA)-1 = }A-1. V. Trace(B) = b11 + b2 + b33 (a) II and II (b) I, II and V (c) II and III (d) IV and V (e) IV

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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a11 a12 a13
b11 b12 b13
Let A
a21 a22 a23 | and B
b21 b22 b23 be given. Which of the following statement or
a31 a32 a33
b31 b32 b33
statements are absolutely correct?
I. If AB = 0, then A = 0 or B = 0.
II. (A+B)² = A²+2AB + B² dir.
a11
a12
a13
III. For k e R, kA = | ka21 ka ka23
a31
a32
a 33
IV. For k + 0, if A-1 exists, then (kA)-1 = }A-1.
V. Trace(B) = b11 + b2 + b33
(a) II and II
(b) I, II and V
(c) II and III
(d) IV and V
(e) IV
Transcribed Image Text:a11 a12 a13 b11 b12 b13 Let A a21 a22 a23 | and B b21 b22 b23 be given. Which of the following statement or a31 a32 a33 b31 b32 b33 statements are absolutely correct? I. If AB = 0, then A = 0 or B = 0. II. (A+B)² = A²+2AB + B² dir. a11 a12 a13 III. For k e R, kA = | ka21 ka ka23 a31 a32 a 33 IV. For k + 0, if A-1 exists, then (kA)-1 = }A-1. V. Trace(B) = b11 + b2 + b33 (a) II and II (b) I, II and V (c) II and III (d) IV and V (e) IV
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