Maiclubk

2021-02-04

Solve the system of equations using Gaussian elimination

4x-8y=12

-x+2y=-3

4x-8y=12

-x+2y=-3

Obiajulu

Skilled2021-02-05Added 98 answers

Step 1

The system of equations is given by,

4x-8y=12

-x+2y=-3

Step 2

Find the solution of system of equations, it is need to write an equivalent matrix equation AX=B .

$\left[\begin{array}{cc}4& -8\\ -1& 2\end{array}\right]\cdot \left[\begin{array}{c}x\\ y\end{array}\right]=\left[\begin{array}{c}12\\ -3\end{array}\right]$

Find the inverse matrix by using Gauss-Jordan elimination method.

That is, apply the row equivalent operations to the matrix.

Consider the matrix$A=\left[\begin{array}{cc}4& -8\\ -1& 2\end{array}\right]$ .

Form of an augment matrix, in order to find the inverse matrix.

That is, form an matrix contains of A on the left side and the$2\times 2$ identify matrix on the right side.

$\left[\begin{array}{ccc}4& -8& 12\\ -1& 2& -3\end{array}\right]$

Step 3

Divide the first row by 4 as follows.

$\left[\begin{array}{ccc}1& -2& 3\\ -1& 2& -3\end{array}\right]$ New row $1=\frac{1}{4}$ row 1

Add the first and second rows as follows.

$\left[\begin{array}{ccc}1& -2& 3\\ 0& 0& 0\end{array}\right]$ New row 2 = row 1 + row 2

Thus, the system of equations has a solution set is$\{x-2y=3.$ .

Step 4

Answer:

The system of equations has a solution set$\{x-2y=3.$ .

The system of equations is given by,

4x-8y=12

-x+2y=-3

Step 2

Find the solution of system of equations, it is need to write an equivalent matrix equation AX=B .

Find the inverse matrix by using Gauss-Jordan elimination method.

That is, apply the row equivalent operations to the matrix.

Consider the matrix

Form of an augment matrix, in order to find the inverse matrix.

That is, form an matrix contains of A on the left side and the

Step 3

Divide the first row by 4 as follows.

Add the first and second rows as follows.

Thus, the system of equations has a solution set is

Step 4

Answer:

The system of equations has a solution set

$\frac{20b}{{\left(4{b}^{3}\right)}^{3}}$

Which operation could we perform in order to find the number of milliseconds in a year??

$60\cdot 60\cdot 24\cdot 7\cdot 365$ $1000\cdot 60\cdot 60\cdot 24\cdot 365$ $24\cdot 60\cdot 100\cdot 7\cdot 52$ $1000\cdot 60\cdot 24\cdot 7\cdot 52?$ Tell about the meaning of Sxx and Sxy in simple linear regression,, especially the meaning of those formulas

Is the number 7356 divisible by 12? Also find the remainder.

A) No

B) 0

C) Yes

D) 6What is a positive integer?

Determine the value of k if the remainder is 3 given $({x}^{3}+k{x}^{2}+x+5)\xf7(x+2)$

Is $41$ a prime number?

What is the square root of $98$?

Is the sum of two prime numbers is always even?

149600000000 is equal to

A)$1.496\times {10}^{11}$

B)$1.496\times {10}^{10}$

C)$1.496\times {10}^{12}$

D)$1.496\times {10}^{8}$Find the value of$\mathrm{log}1$ to the base $3$ ?

What is the square root of 3 divided by 2 .

write $\sqrt[5]{{\left(7x\right)}^{4}}$ as an equivalent expression using a fractional exponent.

simplify $\sqrt{125n}$

What is the square root of $\frac{144}{169}$