The linear equations: [math: 2x−7y=95x=−3]\begin{array}{l}\;2x - 7y = { m{ }}9\\;5x\quad \quad \; = -3\end{array} can be written in matrix form as:

Question

The linear equations: [math: 2x−7y=95x=−3]\begin{array}{l}\;2x - 7y = {m{ }}9\\;5x\quad \quad \; = -3\end{array} can be written in matrix form as:

BlackTom AI · Accepted Answer

The problem asks to write the given linear system in matrix form. The system, interpreted from the text, is:
2x - 7y = 9
5x = -3
This corresponds to the coefficient matrix A consisting of the coefficients of x and y in each equation, the variable vector [x y]^T, and the right-hand side vector b. Thus:
A = [[2, -7], [5, 0]]
[x y]^T is the column vector [x, y]^T
b = [9, -3]^T
So the matrix equation is A [x y]^T = b, or explicitly:
[[2, -7],
 [5, 0]] * [x, y]^T = [9, -3]^T

Now, evaluating the provided option(s):
- The listed option begins with 'b. [math: [2−750]]\left[ {\begin{array}{*{20}{c}}2&{ - 7}\5&0\end{array}} ight][math: [xy]]\left[ {\begin{array}{*{20}{c}}x\y\end{array}} ight]= [math: [9−3]]\left[ {\begin{array}{*{20}{c}}9\{ - 3}\end{array}} ight]'. This appears to be attempting to present the same matrix equation, with the coefficient matrix [[2, -7], [5, 0]] and the right-hand side vector [9, -3], but the formatting is garbled (e.g., '2−750' and mismatched brackets).

- The intended correct structure (if clean) is exactly: [[2, -7], [5, 0]] [x y]^T = [9, -3]^T. The option tries to place the same matrices and vectors, but the extra framing and odd numbers ('2−750') suggest a transcription error or formatting corruption.

Thus, the concept conveyed by the option aligns with the correct matrix form, but the actual text is not clean or reliable as written due to garbled formatting. If you were to assess correctness, you would recognize the proper A, the correct variable vector, and the correct b, while noting the presented garbling should be corrected for unambiguous notation.

In summary, the correct matrix form is [[2, -7], [5, 0]] * [x, y]^T = [9, -3]^T, and the option shown is an attempt at this form but is corrupted in its formatting and should be rewritten clearly to avoid confusion.

MCD1550 / MCD2140 - T1 - 2025 TEST 2 (Week 6)

The linear equations: [math: 2x−7y=95x=−3]\begin{array}{l}\;2x - 7y = {\rm{ }}9\\\;5x\quad \quad \; = -3\end{array} can be written in matrix form as:

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