If P is a 3×3 matrix such that PT=2P+I, where PT is the transpose of P and I is the 3×3 identity matrix, then there exists a column matrix X=⎡⎢⎣xyz⎤⎥⎦≠⎡⎢⎣000⎤⎥⎦ such that
A
PX=X
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
PX=−X
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
PX=⎡⎢⎣000⎤⎥⎦
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
PX=2X
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution
The correct option is BPX=−X PT=2P+I ⇒P=2PT+I ⇒P=2[2P+I]+I ⇒P=4P+3I ⇒3P=–3I ⇒PX=–X