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1203. The following two statements are given for a square matrix A such that A5=0 (I) I+ A is invertible (II) I-A is invertible Of these statements (a) (I) is correct but not (II) (b) (II) is correct but not (I) (c) both (I) and (II) are correct (d) none of (I) and (II) is correct UP RCS (Pre) 2007

1203. The following two statements are given for a square matrix A such that A5=0 (I) I+ A is invertible (II) I-A is invertible Of these statements (a) (I) is correct but not (II) (b) (II) is correct but not (I) (c) both (I) and (II) are correct (d) none of (I) and (II) is correct UP RCS (Pre) 2007

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.2: Linear Independence, Basis, And Dimension
Problem 3AEXP
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1203. The following two statements are given for a square matrix A such that A5 = 0 (I) I + A is invertible (II) I-A is invertible Of these statements (a) (I) is correct but not (II) (b) (II) is correct but not (I) (c) both (I) and (II) are correct (d) none of (I) and (II) is correct IP PCS (Pre) 2007
Transcribed Image Text:1203. The following two statements are given for a square matrix A such that A5 = 0 (I) I + A is invertible (II) I-A is invertible Of these statements (a) (I) is correct but not (II) (b) (II) is correct but not (I) (c) both (I) and (II) are correct (d) none of (I) and (II) is correct IP PCS (Pre) 2007
then. 1171. If 3x3 • matrix A is such that A = 0, then consider the following two statements: यदि कोई 3x3 वर्ग आव्यूह A इस प्रकार हो कि A 0, तो निम्न प्रकथनों पर विचार कीजिये। I: Ib+A is invertible/ I3+A व्युत्क्रमणीय है। II: I3-A is invertible/I3-A व्युत्क्रमणीय है। of these statements: /इन प्रकथनों में: (a) I is correct but II is not correct I सत्य है लेकिन II असत्य है (b) I is not correct But II is correct I असत्य है लेकिन II सत्य है (c) Both I and II are correct दोनों I तथा II सत्य है (d) Both I and II are incorrect दोनों I तथा II असत्य है
Transcribed Image Text:then. 1171. If 3x3 • matrix A is such that A = 0, then consider the following two statements: यदि कोई 3x3 वर्ग आव्यूह A इस प्रकार हो कि A 0, तो निम्न प्रकथनों पर विचार कीजिये। I: Ib+A is invertible/ I3+A व्युत्क्रमणीय है। II: I3-A is invertible/I3-A व्युत्क्रमणीय है। of these statements: /इन प्रकथनों में: (a) I is correct but II is not correct I सत्य है लेकिन II असत्य है (b) I is not correct But II is correct I असत्य है लेकिन II सत्य है (c) Both I and II are correct दोनों I तथा II सत्य है (d) Both I and II are incorrect दोनों I तथा II असत्य है
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