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miskamm [114]
3 years ago
9

Determine the value (or values) of h such that the matrix: 2 - 3 h - 6 9 5 is the augmented matrix of a consistent linear system

.
Mathematics
1 answer:
Verizon [17]3 years ago
5 0

Answer:

In order to have a consistent linear system represented by the augmented matrix:

\left[\begin{array}{ccc}2&-3&h\\-6&9&5\end{array}\right]

the value of h must be:

h=-\frac{5}{3}

Step-by-step explanation:

A system is consistent if it has a solution, this solution can be unique or a set of infinite solutions.  

First, you take the augmented matrix and find the equivalent row echelon form using Gaussian-Jordan elimination:

To do this, you have to multiply the 1st row by 3 and add it to the 2nd row, the resulting matrix is:

\left[\begin{array}{ccc}2&-3&h\\0&0&5+3h\end{array}\right]

Now, write the system of equations:

2x_1-3x_2=h\\0x_1+0x_2=5+3h

The only way this system has a solution is if 5+3h=0, then, to satisfy this, the value of h must be:

h=-\frac{5}{3}

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A line has a gradient of 8 and passes through the point (2,3). Find the equation of the line
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                  - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

\large\blue\textsf{\textbf{\underline{\underline{Question:-}}}}

        A line has a gradient of 8 and passes through (2, 3). What is the line's equation?

\large\blue\textsf{\textbf{\underline{\underline{Answer and How to solve:-}}}}

       With the provided information, we can write the equation of the line in point-slope form:

          \sf{y-y_1=m(x-x_1)}

<u>Where</u>

y₁ = the y-coordinate of the point

m = gradient or slope

x₁ = the x-coordinate of the point

Substitute the values:-

\sf{y-3=8(x-2)}

We have our equation in point-slope form.

If you need the equation in slope-intercept form, please consult the following steps.

\sf{y-3=8(x-2)}

Use the distributive property and multiply 8 times x and -2:-

\sf{y-3=8x-16}

Now, add 3 on both sides:-

\dashrightarrow\star\bigstar\boxed{\sf{y=8x-13}}

<h3>Good luck.</h3>

              - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

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