Answer:
Option C
Step-by-step explanation:
- For the matrix A of order
to be invertible, its determinant must not be equal to zero, |A| 
0, 
exists if- AC = CA = I, where I is identity matrix.
- The homogeneous equation with coefficient matrix A has a unique solution:
AB = 0, B = 
Thus, B = (0, 0, 0......., 0) is a unique solution
2. The non - homogeneous equation system with coefficient matrix A has a unique solution:
For an equation- AY = D
Y = 
is a unique solution
3. Every non homogeneous equation with coefficient matrix A is not consistent as:
For an equation- AY = D, has a solution.l Thus coefficient matrix is inconsistent whereas augmented matrix is.
4. Rank of matrix A = n, Thus the column space of A is 
5. Since, column space of A = , thus x→xA is one-to-one
If 2 + 5i is a zero, then by the complex conjugate root theorem, we must have its conjugate as a zero to have a polynomial containing real coefficients. Therefore, the zeros are -3, 2 + 5i, and 2 - 5i. We have three zeros so this is a degree 3 polynomial (n = 3).
f(x) has the equation
f(x) = (x+3)(x - (2 + 5i))(x - (2 - 5i))
If we expand this polynomial out, we get the simplest standard form
f(x) = x^3-x^2+17x+87
Therefore the answer to this question is f(x) = x^3-x^2+17x+87
probability of drawing ace: 4/52 = 1/13
probability of drawing 9: 4/52 = 1/13
probability of drawing ace or 9: 1/13 + 1/13 = 2/13 or ~15.4%
Answer:
Dilation of 1/2 and then a reflection over y=2
437-456-513-650-893-954-1018-1038-1117-1465
