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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]

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