Since A is a symmetric matrix, \(A = A^T\). This means that \(a_{ij} = a_{ji}\) for all i and j.
From the given matrix, we have the following relationships:
\(a_{12} = a_{21}\), which means \(12 = 6x\). Solving for x, we get \(x = \frac{12}{6} = 2\).
\(a_{13} = a_{31}\), which means \(4y = 8x\). Substituting \(x = 2\), we get \(4y = 8(2) = 16\). Solving for y, we get \(y = \frac{16}{4} = 4\).
\(a_{23} = a_{32}\), which means \(2x = 4\). Substituting \(x = 2\), we get \(2(2) = 4\), which is consistent.
Now, we need to find the value of \(2x + y\). Substituting the values of x and y, we get \(2(2) + 4 = 4 + 4 = 8\).
Correct Answer: 8
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Pedagogical Audit
Bloom's Analysis:
This is an APPLY question because it requires students to apply the definition of a symmetric matrix to find the values of x and y and then calculate 2x+y.
Knowledge Dimension:PROCEDURAL
Justification:The question requires the student to follow a procedure: understanding the properties of symmetric matrices, setting up equations based on those properties, solving for the unknowns, and then substituting those values into the expression 2x+y.
Syllabus Audit:
In the context of CBSE Class 12, this is classified as KNOWLEDGE. The question directly tests the student's understanding and application of the properties of symmetric matrices, a concept covered in the textbook.