Manipal MET2023MathematicsMatrices

If A= [ array cc 2 & -1 -7 & 4 array ] and B= [ array ll 4 & 1 7 & 2 array ] , then B^T A^T is

Options

Anull matrix
Ban identity matrix
Cscalar but not an identity matrix
Dsuch that T_r (B^T A^T )=4

Correct answer

B. an identity matrix

Step-by-step solution

B^T A^T=(A B)^T= ( [ array cc 2 & -1 -7 & 4 array ] [ array cc 4 & 1 7 & 2 array ] )^ = [ array cc 8-7 & 2-2 -28+28 & -7+8 array ]^ = [ array ll 1 & 0 0 & 1 array ]^ = [ array ll 1 & 0 0 & 1 array ]=I

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