Question

4x-2y+6z=8, x+y-3z=-1, 15x-3y+9z=21 The rank of the coefficient matrix isRequired to answer. Single choice.

(1 Point)

1

4

2

3

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Answer 1

Answer:

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Each of your kidneys is made up of about a million filtering units called nephrons. Each nephron includes a filter, called the glomerulus, and a tubule. ... Each nephron has a glomerulus to filter your blood and a tubule that returns needed substances to your blood and pulls out additional wastes.

Answer 2

The rank of the coefficient matrix is 2

Given,

The equations:

4x-2y+6z= 8,

x+y-3z= -1,

15x-3y+9z= 21

To find,

The rank of the coefficient matrix

Solution,

Representing the given equations in the matrix form,

The matrix form of the system is AX = B, we get.,

A = $\left[\begin{array}{ccc}4&-2&6\\1&1&-3\\15&-3&9\end{array}\right]$ , X = $\left[\begin{array}{ccc}x\\y\\z\end{array}\right]$ , B = $\left[\begin{array}{ccc}8\\-1\\21\end{array}\right]$

By applying the elementary row operations on the augmented matrix [ A | B], we get., (the process is mentioned in the picture attached below)

To find the rank of any matrix, we must transform that matrix into its echelon form and then determine the rank by the number of non-zero rows.

Here, ρ ( A) = ρ ([ A | B]) = 2 < 3

and from the echelon form, we get the equivalent equations

x + y - 3z  =  -1, y - 3z = -2 , 0 = 0

The number of non-zero rows is 2

Hence, the rank of a matrix is 2

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