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
Answer:
The rate of the current is 2 miles per hour.
Step-by-step explanation:
Let us assume that the rate of the river is v miles per hour.
The speed of the boat is 12 miles per hour.
Let us assume also that the boat can go 21 miles in t hours in the downstream and 15 miles upstream at the same time i.e. t hours.
So, from the condition given we can write that
......... (1), and
......... (2)
Now, adding those two equations we get
⇒ 
hours
Now, from equation (1), we get,
⇒ v = 2 miles per hour
Therefore, the rate of the current is 2 miles per hour. (Answer)
Just take 1 divided by 6
1/6=0.16666667
Answer:
2n+7
Step-by-step explanation:
find the difference
and see the difference from the 2 Times table to the original sequence
and write it as an equation for this sequence
Answer:
Step-by-step explanation:
Equation
L = a + (n - 1)*d
Givens
L = 55
a = 13
n =8
Solution
55 = 13 + (8 - 1)*d Combine
55 = 13 + 7d Subtract 13 from both sides
55 - 13 = 7d
42 = 7d Divide by 7
d = 6
