Answer:
The correct option is (A).
Step-by-step explanation:
If the reduced row echelon form of the coefficient matrix of a linear system of equations in four different variables has a pivot, i.e. 1, in each column, then the reduced row echelon form of the coefficient matrix is say A is an identity matrix, here I₄, since there are 4 variables.
![\left[\begin{array}{cccc}1&0&0&0\\0&1&0&0\\0&0&1&0\\0&0&0&1\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D1%260%260%260%5C%5C0%261%260%260%5C%5C0%260%261%260%5C%5C0%260%260%261%5Cend%7Barray%7D%5Cright%5D)
Then the corresponding augmented matrix [ A|B] , where the matrix is the representation of the linear system is AX = B, must be:
![\left[\begin{array}{ccccc}1&0&0&0&a\\0&1&0&0&b\\0&0&1&0&c\\0&0&0&1&d\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccccc%7D1%260%260%260%26a%5C%5C0%261%260%260%26b%5C%5C0%260%261%260%26c%5C%5C0%260%260%261%26d%5Cend%7Barray%7D%5Cright%5D)
Now the given linear system is consistent as the right most column of the augmented matrix is a linear combination of the columns of A as the reduced row echelon form of A has a pivot in each column.
Thus, the correct option is (A).
Answer:
85
Step-by-step explanation:
<em>The equation for the discriminant is </em>
b^2-4(a)(c)
<em>Plug your numbers in from the equation. </em>
<em>1=a, -7=b, -9=c</em>
<em />
(-7)^2-4(1)(-9)
49-(-36)
49+36
85
To find the perimeter of the square, you add all four sides together:
10x + 10x + (6x + 8) + (6x + 8)
20x + 12x + 16 = P
32x + 16 = P
you have to find x to get the actual perimeter. Since the shape is a square, all 4 sides are equal, so you can set 10x and (6x + 8) as equal to each other.
10x = 6x + 8
4x = 8
x = 2
Now you just plug in x and finish the rest of the problem, and you have the answer:
32(2) + 16 = P
64 + 16 = P
P = 80
(if you find this helpful, marking this as the brainliest answer would make my day :)
Answer:
6
Step-by-step explanation:
4
Answer: $525
Step-by-step explanation:
The formula for Simple interest is calculated as PRT where
P = Principal = $7500
R = Rate = 3.5%
T = Time = 2 years
Interest = PRT
= 7500 × 3.5% × 2
= 7500 × 0.035 × 2
= $525
