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Questions › UoH › UoH 2020 › Q12
1 mark, −0.33Mathematics › Matrices, determinants and linear systems › Singular matrices and invertibilityModerateabout 1 min

UoH 2020 Question 12: Matrices, determinants and linear systems

Let A be an upper triangular matrix of order nnn with diagonal elements aii≠0a_{ii} \neq 0aii​=0 for all i=1,2,…ni = 1, 2, \ldots ni=1,2,…n and trace(A)=0trace(A) = 0trace(A)=0. Then,

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Let A be an upper triangular matrix of order n with diagonal elements aᵢᵢ ≠ 0 for all i = 1, 2, … n and trace(A) = 0. Then, (A) A is non-singular (B) A is a positive definite matrix (C) A is idempotent (D) A is a negative definite matrix

Also written as: Let A be an upper triangular matrix of order n with diagonal elements a_(ii) != 0 for all i = 1, 2,... n and trace(A) = 0. Then,

Matrices, determinants and linear systems has come up 102 times in 7 exams since 2006.

What this question tests

This question is on Singular matrices and invertibility, part of Matrices, determinants and linear systems in Mathematics.

When a matrix has an inverse and what singularity means.

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