Answered

Discover the best answers at Westonci.ca, where experts share their insights and knowledge with you. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A platform. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.

Given
[tex]\[ A = \left[\begin{array}{cc}2 & -7 \\ 6 & 1\end{array}\right] \][/tex]
and
[tex]\[ B = \left[\begin{array}{cc}-9 & 5 \\ 1 & -1\end{array}\right]. \][/tex]

If [tex]\( X - A = B \)[/tex], what is [tex]\( X \)[/tex]?

A. [tex]\(\left[\begin{array}{cc}-7 & -2 \\ 7 & 0\end{array}\right]\)[/tex]

B. [tex]\(\left[\begin{array}{cc}-11 & 12 \\ -5 & -2\end{array}\right]\)[/tex]

C. [tex]\(\left[\begin{array}{cc}-7 & -12 \\ 5 & 0\end{array}\right]\)[/tex]

D. [tex]\(\left[\begin{array}{ll}11 & -12\end{array}\right]\)[/tex]

Sagot :

GinnyAnswer
To find [tex]\(X\)[/tex] given the equation [tex]\(X - A = B\)[/tex], we first need to isolate [tex]\(X\)[/tex]. We can do this by adding matrix [tex]\(A\)[/tex] to both sides of the equation. The step-by-step solution is as follows:

Given the equation:
[tex]\[ X - A = B \][/tex]

Add matrix [tex]\(A\)[/tex] to both sides:
[tex]\[ X = A + B \][/tex]

Now, let's find the matrices [tex]\(A\)[/tex] and [tex]\(B\)[/tex] and then add them together.

Matrix [tex]\(A\)[/tex] is:
[tex]\[ A = \begin{pmatrix} 2 & -7 \\ 6 & 1 \end{pmatrix} \][/tex]

Matrix [tex]\(B\)[/tex] is:
[tex]\[ B = \begin{pmatrix} -9 & 5 \\ 1 & -1 \end{pmatrix} \][/tex]

To find [tex]\(X\)[/tex], we add matrices [tex]\(A\)[/tex] and [tex]\(B\)[/tex] element-wise:
[tex]\[ X = \begin{pmatrix} 2 & -7 \\ 6 & 1 \end{pmatrix} + \begin{pmatrix} -9 & 5 \\ 1 & -1 \end{pmatrix} \][/tex]

Calculate each element of [tex]\(X\)[/tex]:

1. The element in the first row and first column of [tex]\(X\)[/tex] is:
[tex]\[ 2 + (-9) = -7 \][/tex]

2. The element in the first row and second column of [tex]\(X\)[/tex] is:
[tex]\[ -7 + 5 = -2 \][/tex]

3. The element in the second row and first column of [tex]\(X\)[/tex] is:
[tex]\[ 6 + 1 = 7 \][/tex]

4. The element in the second row and second column of [tex]\(X\)[/tex] is:
[tex]\[ 1 + (-1) = 0 \][/tex]

Therefore, the matrix [tex]\(X\)[/tex] is:
[tex]\[ X = \begin{pmatrix} -7 & -2 \\ 7 & 0 \end{pmatrix} \][/tex]

So, the correct answer is:
[tex]\[ \boxed{\begin{pmatrix}-7 & -2 \\ 7 & 0\end{pmatrix}} \][/tex]
Hi1315

Answer:

A

Step-by-step explanation:

To find  X  given that  X - A = B , we can rearrange the equation to solve for  X :

X = A + B

Let's calculate  A + B :

Given:

A =[tex]\left[\begin{array}{cc} 2 & -7 \\ 6 & 1 \end{array}\right][/tex]

and

B = [tex]\left[\begin{array}{cc} -9 & 5 \\ 1 & -1 \end{array}\right][/tex]

Add the corresponding elements of matrices  A  and  B :

[tex]X = \left[\begin{array}{cc} 2 & -7 \\ 6 & 1 \end{array}\right] + \left[\begin{array}{cc} -9 & 5 \\ 1 & -1 \end{array}\right] \\\\ \left[\begin{array}{cc} 2 + (-9) & -7 + 5 \\ 6 + 1 & 1 + (-1) \end{array}\right] \\\\ \left[\begin{array}{cc} -7 & -2 \\ 7 & 0 \end{array}\right][/tex]

Therefore, the correct answer is:

A.[tex]\left[\begin{array}{cc} -7 & -2 \\ 7 & 0 \end{array}\right][/tex]

Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Get the answers you need at Westonci.ca. Stay informed with our latest expert advice.