A square matrix P satisfies P² = I - P , where I is identity matrix . If P = 5I − 8P¸ then n is : (a) 4 ¸ (b) 5 ¸ (c) 6 ¸ (d) 7

Asked by yeeshuraj3 | 13th Sep, 2016, 01:56: PM

Expert Answer:

straight P squared equals straight I minus straight P
straight P to the power of 4 equals open parentheses straight P squared close parentheses open parentheses straight P squared close parentheses equals open parentheses straight I minus straight P close parentheses open parentheses straight I minus straight P close parentheses equals straight I plus straight P squared minus 2 straight P equals straight I plus straight I minus straight P minus 2 straight P equals 2 straight I minus 3 straight P
straight P to the power of 6 equals open parentheses straight P to the power of 4 close parentheses open parentheses straight P squared close parentheses equals open parentheses 2 straight I minus 3 straight P close parentheses open parentheses straight I minus straight P close parentheses equals 2 straight I minus 2 straight P minus 3 straight P plus 3 straight P squared equals 2 straight I minus 2 straight P minus 3 straight P plus 3 straight I minus 3 straight P equals 5 straight I minus 8 straight P

So space straight n space equals space 6

Answered by Vijaykumar Wani | 14th Sep, 2016, 01:05: PM