1. What is the determinant of the matrix?
[5 6]
[2 9]
a. -33
b. 6
c. -6
d. 33 <---- my answer
2. What is the determinant of the matrix?
[-4 -5]
[ 2 -6]
a. -14
b. -34
c. 14
d. 34 <---- my answer
3. Which expression gives the x-coordinate of the solution of the system?
2x+3y=5
3x+5y=7
a.
|2 5|
|3 7|
________
|2 3|
|3 5|
b.
|2 5|
|3 7|
________
|5 3|
|7 5|
c.
|5 2|
|7 3|
________
|2 3|
|3 5|
d.
|5 3|
|7 5|
________
|2 3|
|3 5|
I agree with your first two answers.
Do you have an answer for the 3rd one?
D =
|2 3|
|3 5|
so B is out
Replace the 1st column with (5,7) and that gives D.
To find the determinant of a 2x2 matrix, you can use the formula:
Det(A) = (a*d) - (b*c)
Let's apply this formula to the given matrices:
1. For the matrix: [5 6] [2 9]
[2 9]
The values of a, b, c, and d are:
a = 5, b = 6, c = 2, and d = 9.
Using the determinant formula, we have:
Det(A) = (5*9) - (6*2) = 45 - 12 = 33
Therefore, the determinant of the first matrix is 33.
Looking at the answer choices, d. 33 is correct.
2. For the matrix: [-4 -5] [ 2 -6]
[ 2 -6]
The values of a, b, c, and d are:
a = -4, b = -5, c = 2, and d = -6.
Using the determinant formula, we have:
Det(A) = (-4*-6) - (-5*2) = 24 + 10 = 34
Therefore, the determinant of the second matrix is 34.
Looking at the answer choices, d. 34 is correct.
3. For the system of equations:
2x + 3y = 5
3x + 5y = 7
To find the x-coordinate of the solution, we can use Cramer's Rule, which involves finding the determinant of matrices formed with coefficients of x and y (A_x) and constants (A_y).
The matrix A_x is formed by replacing the coefficients of x with the constants:
|5 3|
|7 5|
To find the determinant of A_x, we use the determinant formula as described earlier.
The matrix A_y is formed by placing the constants on the right-hand side of the equations:
|2 3|
|3 5|
To find the determinant of A_y, we use the determinant formula again.
Now, let's find the determinants:
Det(A_x) = (5*5) - (3*7) = 25 - 21 = 4
Det(A_y) = (2*5) - (3*3) = 10 - 9 = 1
The x-coordinate can be found by dividing Det(A_x) by Det(A_y):
x = Det(A_x) / Det(A_y) = 4/1 = 4
Therefore, the expression that gives the x-coordinate of the solution is:
|5 3|
|7 5|
Looking at the answer choices, a.|2 5| |3 7| is the correct matrix.