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.

$\left[\begin{array}{cccc}1&0&0&0\\0&1&0&0\\0&0&1&0\\0&0&0&1\end{array}\right]$

Then the corresponding augmented matrix [ A|B] , where the matrix is the representation of the linear system is AX = B, must be:

$\left[\begin{array}{ccccc}1&0&0&0&a\\0&1&0&0&b\\0&0&1&0&c\\0&0&0&1&d\end{array}\right]$

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).

8 0

3 years ago

15t +95 + 5 - 9<br> i need help please

photoshop1234 [79]

15t + 95 + 5 - 9 = 106t

8 0

3 years ago

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Craig has a 6 ft by 6 ft square garden in his backyard. He wants to transform the garden into a rectangular shape and reduce the

Yanka [14]

X = 2
So 6 + 2 = 8
6 - 2 = 4
8 x 4 = 32

(6-x)(6+x) = 32
36 - x^2 = 32
-36. -36
-x^2 = -4
X = 2

7 0

3 years ago

(x^2 + 9x + 22) ÷ (x+2) dividing polynomials​

(x^2 + 9x + 22) ÷ (x+2) dividing polynomials