Question
Question: If D = diag [d<sub>1</sub>, d<sub>2</sub>, .....d<sub>n</sub>] is a diagonal matrix with d<sub>i</s...
If D = diag [d1, d2, .....dn] is a diagonal matrix with
di ¹ 0, i = 1, 2, 3,......, n, then D–1 is
A
d1−1 d2−1......dn−1In
B
diag [dn−1,dn−1−1, ....... d1−1]
C
diag [d1−1 d2−1......dn−1]
D
None of these
Answer
diag \mathrm { d } _ { 1 } ^ { - 1 }$$d_{2}^{- 1}$......$d_{n}^{- 1}
Explanation
Solution
Here |D| = d1d2d3 ........dn and
adj D = [d2d3 ........dn, d1d3.........dn, ........ d1d2.......dn–1]
Ž D–1 = diag [d1−1,d2−1....... dn−1]