Answer:
30
Step-by-step explanation:
To find the determinant of a 3x3 matrix, you can use this method. (See picture.)
Start with the first number in the top row, and block off the row and column. A 2x2 matrix will be left. Find the determinant of this 2x2 matrix, and multiply it by the number in the top row.
Repeat for the other two numbers in the top row. Add the first result, subtract the second, and add the third.
det A = -2 [(3)(-5) − (a)(0)] − 2 [(0)(-5) − (a)(0)] + b [(0)(0) − (3)(0)]
det A = -2 (3)(-5) − 0 + 0
det A = 30
Answer:
40
Step-by-step explanation:
Any solution x will mod 23 will also have x+23n as a solution, for some integer n. Since 900/23 = 39 3/23, we know there are 39 or 40 three-digit integers of this form.
As it happens, 100 is the smallest 3-digit solution. So, there are 40 three-digit numbers that are of the form 100 +23n, hence 40 solutions to the equation.
_____
The equation reduces, mod 23, to ...
10x = 11
Its solutions are x = 23n +8.
The answer is about 13.9927.
You would divide 52/11 and then subtract that decimal by 18.65.
18.65-4.7272=13.9927.
12/6 is 2
2 +2 is 4
The overall answer is 4