Fundamental of Matrices Quiz

What is the determinant of a matrix A if

• 6

• 1

• -14

• 8

Which of the following is a property of the transpose of a matrix?

• A^T * B^T = (AB)^T

• (A^T)^T = A

• A^T + B^T = (A + B)^T

• All of the above

Which of the following matrix is singular?

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What is the condition for a matrix to be non-singular?

• Its determinant is zero

• It has infinite solutions

• Its determinant is non-zero

• It has no inverse

• The product of the elements in the jth column

• The trace of the matrix

• The sum of the elements in the ith row

• The determinant of the matrix obtained by deleting the i^th row and j^th column

What is the result of multiplying a matrix A by its adjoint?

• I

• A

• 0

Which of the following statements is true about the inverse of a matrix?

• Inverse matrices are always singular

• All matrices have inverses

• Non-singular matrices have unique inverses

• Only singular matrices have inverses

What is the adjoint of the matrix A ?

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• 
• 

What is the inverse of the matrix A ?

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• 
• 
• 

What is the cofactor C₂₃ of the matrix A ?

• 4

• -4

• 2

• -2