Option (D) is correct after using the concept of the inverse of a matrix.
What is the matrix?
It is defined as the group of numerical data, functions, and complex numbers in a specific way such that the representation array looks like a square, rectangle shape.
The question is incomplete.
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It is given that:
The pair of linear equation in two variables can be solved by the matrix method and the matrix equation is given;
\(\rm \left[\begin{array}{ccc}1/2&-1/4\\2&-3/4\\\end{array}\right] \left[\begin{array}{ccc}x\\y\\\end{array}\right] =\left[\begin{array}{ccc}2&-4\\1&6\\\end{array}\right]\)
Let A, X, and B are the matrix
We can write as:
AX = B
or
X = A⁻¹B
Here A⁻¹ is the inverse of the matrix
After solving:
\(\rm X= \right] \left[\begin{array}{ccc}x\\y\\\end{array}\right]\)
\(\rm A^{-1} =\left[\begin{array}{ccc}-6&2\\-16&4\\\end{array}\right] \left\)
\(\rm B = \right] \left[\begin{array}{ccc}2&-4\\1&6\\\end{array}\right]\)
\(\rm \right] \left[\begin{array}{ccc}x\\y\\\end{array}\right] =\left[\begin{array}{ccc}-6&2\\-16&4\\\end{array}\right] \left[\begin{array}{ccc}2&-4\\1&6\\\end{array}\right]\)
Thus, option (D) is correct after using the concept of the inverse of a matrix.
Learn more about the matrix here:
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