Matrices And DeterminantsMathematics

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Question 1
MediumJEE

A is a three by three matrix with determinant two. What is the determinant of three A?

A. 6
B. 18
C. 27
D. 54
Question 2
MediumJEE

The homogeneous system x-cy-cz=0, cx-y+cz=0, cx+cy-z=0 has a non-trivial solution. What is the greatest possible value of c?

A. 1-1
B. 1/2-1/2
C. 1/21/2
D. 1
Question 3
HardJEE

The system x-2y+3z=9, 2x+y+z=b, x-7y+a z=24 has infinitely many solutions. Find a-b.

A. 3
B. 4
C. 5
D. 6

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