If A = is a symmetric matrix, the value of k is _______.
Correct Answer :
8
Solution :
The correct option is 8.
To find the value of , let us first recall the definition of a symmetric matrix. A square matrix is symmetric if it is equal to its transpose, which means . For a matrix of the form:
the symmetry condition requires that the off-diagonal elements are equal, i.e., .
Given the matrix:
the off-diagonal elements are:
and
.
Setting these two elements equal to each other gives the following linear equation:
To solve for , we subtract from both sides of the equation:
Next, we add to both sides of the equation:
Thus, the value of that makes the matrix symmetric is indeed 8.
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