Engineering Board Exam Reviewer · Matrix Inverse and Cofactors · hard
Find the sum of all entries of A-1 if A= bmatrix2&1&0\1&2&1\0&1&2 bmatrix.
- 4
- 0.25
- 2
- 1
Answer
D. 1
Solution
A=2(4-1)-1(2-0)=4 and adj,A= bmatrix3&-2&1\-2&4&-2\1&-2&3 bmatrix, so A-1= 14 adj,A. The entries of adj,A add to 3-2+1-2+4-2+1-2+3=4, so the sum of the entries of A-1 is 44=1.
More Matrix Inverse and Cofactors questions
- Find the (1,2) entry of A-1 if A= bmatrix1&2&1\0&1&3\2&1&0 bmatrix.
- Find the cofactor C23 of A= bmatrix2&1&3\0&4&-1\5&2&6 bmatrix.
- Find the inverse of A= bmatrix5&2\4&3 bmatrix.
- Find the inverse of A= bmatrix2&1\5&3 bmatrix.
- Find the inverse of A= bmatrix4&7\2&6 bmatrix.
- Find the cofactor C12 of the matrix bmatrix1&2&3\4&5&6\7&8&10 bmatrix.
- For the matrix A= bmatrix3&2\1&4 bmatrix, find the cofactor matrix.
- For A= bmatrix2&1\5&3 bmatrix (with (A)=1), what should A· A-1 equal?
- A 2×2 matrix has determinant 0. Does it have an inverse?