GATE EC 2023 Set 1 — Question 38
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Engineering Mathematics → Linear Algebra → Matrix Algebra
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Question
Let be an real column vector with length . The trace of the matrix is
Correct answer
(A) l²
Solution
The trace of a matrix is the sum of its diagonal elements. For a product of two matrices and , the property holds if the dimensions allow both products.
Here, , where is and is .
.
Since is a matrix (a scalar), its trace is simply the value of the scalar itself.
Given , we have .
Therefore, .
Here, , where is and is .
.
Since is a matrix (a scalar), its trace is simply the value of the scalar itself.
Given , we have .
Therefore, .
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