Multiple choice

Real matrices [A]3×1, [b]3×3, [C]3×5, [D]5×3, [E]5×5, [F]5×1 are given. Matrices [B] and [E] symmetric. Following statements are made with respect to these matrices. (I) Matrix product [F]T [C]T [B] [C] [F] is a scalar. (II) Matrix product [D]T [F] [D] is always symmetric. With reference to above statements, which of the following applies?

  1. Statement I is true but II is false.

  2. Statement I is false but II is true.

  3. Both the statements are true.

  4. Both the statements are false.
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A Correct answer
Explanation

Statement I: F(T) is 1x5, C(T) is 5x3, B is 3x3, C is 3x5, F is 5x1. The product (1x5)(5x3)(3x3)(3x5)(5x1) results in a 1x1 matrix (scalar). Statement II: D(T) is 3x5, F is 5x1, D is 5x3. The product (3x5)(5x1)(5x3) is a 3x3 matrix, but it is not necessarily symmetric because F is not a symmetric matrix.

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