Aspire's Library
A Place for Latest Exam wise Questions, Videos, Previous Year Papers,
Study Stuff for MCA Examinations - NIMCET
Study Stuff for MCA Examinations - NIMCET
Previous Year Question (PYQs)
If $A = \begin{bmatrix} 3 & -2 \\ 4 & -2 \end{bmatrix}$ satisfies the matrix equation $A^2 - kA + 2I = 0$, then the value of $k$ is:
Solution
Trace of $A = 3 + (-2) = 1$
Determinant of $A = (3)(-2) - (-8) = -6 + 8 = 2$
Characteristic equation of $A$ is:
$\lambda^2 - (\text{trace})\lambda + \det = 0$
$\lambda^2 - \lambda + 2 = 0$
By Cayley–Hamilton theorem:
$A^2 - A + 2I = 0$
Comparing with $A^2 - kA + 2I = 0$
$k = 1$
Online Test Series, Information About Examination,
Syllabus, Notification
and More.
View More
Online Test Series, Information About Examination,
Syllabus, Notification
and More.
View More
Ask Your Question or Put Your Review.
