+128474 Here's 10, Paypay.......this one is more complicated.......there are at least two other ways to do this, but the one presented is more "mechanical"
Here's the procedure
Let's find the determinant of your matrix, first
1 0 1 1 0
1 1 -4 1 1
0 1 -4 0 1
Multiply down the diagonals, sum the products
[(1*1 *-4 + 0 + 1] = [-4 + 1] = -3
Multiply up the diagonals, sum the products
[0 + 1*-4*1 + 0] = -4
Subtract the second thing from the first -3 - (-4) = 1
That's nice.......we don't even need to worry about the det, now !!!!
Now......we take each of the determinants specified in the "formula" and put the results in the proper places
Note.....since the given answers all have the same top row.......we can ignore this.....let's fill in the rest, staring with the second row
So.......filling in and evaluating we have
element 21 = a23 a21 = [-4*0] - [1 *-4] = 4
a33 a31
Npw.....we can eliminate F and J as answers since element 21 in both = -4
The next elemnent, 22, is the same in G and H....so let's calculate element 23
element 23 = a13 a11 = [1*1] - [1*-4] = 5
a23 a21
Then.....H looks to be correct.....!!!
I have verified this using this app :http://matrix.reshish.com/inverCalculation.php
In general....another method kown as "Gaussian Elimination" requires WAY less memorization, but it's easy to make mistskes amd you have to deal with some nasty fractions, at times....!!!
+4082 Sorry to say this, but I'm tired of matrix... I dunno what that is, but you had like three of them last night.......
+128474 Here's 9
The inverse of a 2 x 2 matrix in this form a b is given by :
c d
[1 / det of the matrix] x [ d - b
-c a ]
The determinant of the given matrix = [2 *3] - [-5 * 5] = 6 + 25 = 31
So we have
[1/ 31] x [3 - 5 = [ 3/31 -5/31
5 2 ] 5/31 2/31 ]
(B) is correct
+128474 Here's 10, Paypay.......this one is more complicated.......there are at least two other ways to do this, but the one presented is more "mechanical"
Here's the procedure
Let's find the determinant of your matrix, first
1 0 1 1 0
1 1 -4 1 1
0 1 -4 0 1
Multiply down the diagonals, sum the products
[(1*1 *-4 + 0 + 1] = [-4 + 1] = -3
Multiply up the diagonals, sum the products
[0 + 1*-4*1 + 0] = -4
Subtract the second thing from the first -3 - (-4) = 1
That's nice.......we don't even need to worry about the det, now !!!!
Now......we take each of the determinants specified in the "formula" and put the results in the proper places
Note.....since the given answers all have the same top row.......we can ignore this.....let's fill in the rest, staring with the second row
So.......filling in and evaluating we have
element 21 = a23 a21 = [-4*0] - [1 *-4] = 4
a33 a31
Npw.....we can eliminate F and J as answers since element 21 in both = -4
The next elemnent, 22, is the same in G and H....so let's calculate element 23
element 23 = a13 a11 = [1*1] - [1*-4] = 5
a23 a21
Then.....H looks to be correct.....!!!
I have verified this using this app :http://matrix.reshish.com/inverCalculation.php
In general....another method kown as "Gaussian Elimination" requires WAY less memorization, but it's easy to make mistskes amd you have to deal with some nasty fractions, at times....!!!
