linear algebra

Which of the following is a scalar quantity?

• A row vector

• A single numbeR

• A column vector

• A matrix

The determinant of a 2×2 matrix
[acbd] is:

• a+b+c+d

• ab−cd

• ad−bc

• ac−bd

The dot product of two orthogonal vectors is:

• 0

• 1

• -1

• Undefined

Eigenvalues of an identity matrix are always:

• Both 1 and -1

• -1

• 0

• 1

Which of the following is true for symmetric matrices?

• A2=I

• A=−AT

• A=AT

• AT=0

If vector u=(3,4), then its magnitude is:

• 5

• 25

• 12

• 7

 The inverse of the identity matrix is:

• Zero matrix

• Not defined

• Determinant of the matrix

• Identity matrix itself

 If two vectors are linearly dependent, it means:

• One is a scalar multiple of the other

• They have the same magnitude

• They must be orthogonal

• They are perpendicular

Which of the following is a property of determinants?

• det(A)=det(AT)−1

• det(A+B)=det(A)⋅det(B)

• det(AB)=det(A)⋅det(B)

• det(AB)=det(A)+det(B)

The eigenvalues of a triangular matrix (upper or lower) are:

• Always zero

• Equal to the trace

• Equal to its diagonal elements

• Equal to the determinant