Find the inverse of the matrix, if possible.
A = { 0 -6 }
{-2 -5}
A. 0 -1/2
-1/6 5/12
B. -1/6 0
5/12 - 1/2
C. 5/12 - 1/2
-1/6 0
D. 5/12 1/2
1/6 0
C ?
well, it may be time to ask what method you are supposed to use.
for example you seem to have Cramer's rule so
A * A*-1 = 1 0 over 0 1
so
solve with 1 over 0 on the right
then with 0 over 1 on the right
so for first column of inverse solve
+0 x - 6 y = 1
-2 x - 5 y = 0
then for second column solve
+0 x - 6 y = 0
-2 x - 5 y = 1
left determinant is
D = -12
first solution is for
+1 -6
+0 -5 or -5/12 = element 11
then
+0 +1
-2 +0 over -12
or
2/-12 = -1/6 = A21
then
do the second
1/12 ?
LOL, I have not finished
You need to do the whole ting
all you know is termm 11 and 21 so far
whoops 12 not +12
so
element 11 is 5/12 and element 21 is -1/6
looks like C
LOL You got me confused because I said my answer was C in the first place lmao , THANK YOU !!
To find the inverse of a matrix, you can follow these steps:
1. Calculate the determinant of the matrix A. The determinant of a 2x2 matrix A = [a b; c d] is given by the formula ad - bc, where a, b, c, and d are the elements of the matrix.
For matrix A = { 0 -6; -2 -5 }, the determinant is (0 * -5) - (-6 * -2) = 0 + 12 = 12.
2. Determine if the matrix is invertible. If the determinant is non-zero, then the matrix is invertible. In this case, since the determinant is 12, the matrix is invertible.
3. Calculate the adjugate of the matrix A. The adjugate is the transpose of the matrix of cofactors. To find the matrix of cofactors, you need to calculate the cofactor of each element of the matrix A.
The cofactor of an element is given by the formula (-1)^(i+j) * Mij, where i and j are the row and column indices of the element, and Mij is the determinant of the submatrix obtained by removing the i-th row and j-th column from the original matrix A.
For matrix A = { 0 -6; -2 -5 }, the matrix of cofactors is { -5 -2; -6 0 }, which is obtained by swapping the sign of the elements in the second row and taking the transpose.
Therefore, the adjugate of matrix A is { -5 -6; -2 0 }.
4. Calculate the inverse of the matrix A. The inverse of a matrix A is given by A^(-1) = (1/det(A)) * adj(A), where det(A) is the determinant of A, and adj(A) is the adjugate of A.
Since det(A) is 12, the inverse of matrix A is (1/12) * { -5 -6; -2 0 }.
By simplifying the inverse, we get:
(1/12) * { -5 -6; -2 0 } = { -5/12 -1/2; -1/6 0 }
So, the correct answer is option C.