MATHEMATICS HIGH SCHOOL

Solve the following system using a matrix.

7a - b = -1
-4a - 2b = -2

Answers

Answer 1

Answer:

Answer:

a = 0, b = 1

Step-by-step explanation:

Given system equation is,

7a - b = -1

-4a - 2b = -2

Since, the matrix form of this system of equation is,

$\begin{bmatrix} 7& -1\n -4 & -2\end{bmatrix}\begin{bmatrix}a\nb\end{bmatrix}=\begin{bmatrix}-1\n -2\end{bmatrix}$

Let,

$A=\begin{bmatrix} 7& -1\n -4 & -2\end{bmatrix}$

$X=\begin{bmatrix}a\n b\end{bmatrix}$

$B=\begin{bmatrix}-1\n -2\end{bmatrix}$

$\because AX = B\implies X = A^(-1)B$

$adj(A) = \begin{bmatrix} -2& 1\n4& 7\end{bmatrix}$

Also,

|A| = -18

$\implies A^(-1)=-(1)/(18)\begin{bmatrix} -2& 1\n4& 7\end{bmatrix}$

$\implies X = -(1)/(18)\begin{bmatrix} -2& 1\n4& 7\end{bmatrix}.\begin{bmatrix}-1\n -2\end{bmatrix}$

$X=-(1)/(18)\begin{bmatrix}2-2\n -4-14\end{bmatrix}$

$X=-(1)/(18)\begin{bmatrix}0\n -18\end{bmatrix}$

$X=\begin{bmatrix}0\n 1\end{bmatrix}$

$\implies \begin{bmatrix}a\n b\end{bmatrix}=\begin{bmatrix}0\n 1\end{bmatrix}$

By comparing,

a = 0, b = 1

Answer 2

Answer:

1. a=-1+b/7 is the right answer. First you had to add by b from both sides of equation, and it gave us, $7a-b+b=-1+b$ . And then simplify, and it gave us, $7a=-1+b$ . Divide by 7 from both sides of equation, and it gave us, $(7a)/(7)=-(1)/(7)+ (b)/(7)$ . Finally simplify, and it gave us the answer is a=-1+b/7 is the right answer.

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2. a=-b-1/2 is the right answer. First you had to add by 2b from both sides of equation, and it gave us, $-4a-2b+2b=-2+2b$ . And then simplify, and it gave us, $-4a=-2+2b$ . Next you can also divide by -4 from both sides of equation, and it gave us, $(-4a)/(-4)=-(2)/(-4)+(2b)/(-4)$ . Finally simplify, and it gave us the answer is a=-b-1/2 is the right answer. Hope this helps! And thank you for posting your question at here on brainly, and have a great day. -Charlie

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Answers

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Answers

Answer:

Option 2 is correct.

Step-by-step explanation:

We have been given points of g(x) and f(x)

g(x) has ordered pairs (0,1) ,(1,2) ,(3,8) ,(5,32) and (6,64) this is an exponential function which is $g(x)=2^x$ from the given points.

f(x) has ordered pairs (0,1) ,(1,2) ,(3,10) ,(5,26) and (6,37) this is a quadratic function

We will put these values in the quadratic function which is:

$ax^2+bx+c=y$

Taking (0,1)

$a(0)+b(0)+c=1$

c=1

Now, taking (1,2)

$a+b+1=2$

$a+b=1$ (1)

Now, taking (3,10)

$a(3)^2+b(3)+1=10$

$9a+3b=9$ (2)

Now, solving the equation (1) and (2) we get:

a=1 and b=0

Hence, the function $f(x)=x^2+1$

Please look at the attachment for the graph

We can see that the g(x) an exponential function will eventually exceed the increasing quadratic function

Therefore, option 2 is correct.

Which word shares a word root with remember?revisit
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Answers

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Answer:

( D) Memory

Step-by-step explanation:

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Answers

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Answers

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Answer:2

Step-by-step explanation:

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