Matrix Q/A7: Proving 𝐴2 − 5 𝐴 − 2 𝐼 = 0; Step-by-Step Matrix Solution

Hello amazing people! It’s another beautiful day to deepen our understanding of Mathematics by solving exam problems. In today’s video, I provided a detailed solution to a matrix question where matrix A was given, and we were asked to verify that the expression A² − 5A − 2I = 0.

The first step I took was to determine the matrices for each term in the expression. For A², I obtained the elements [7, 10, 15, 22]. For 5A, the elements were [5, 10, 15, 20], and for 2I, we had [2, 0, 0, 2].

Next, I substituted the matrices for A² and 5A into the expression and performed the calculations, which gave me the matrix [2, 0, 0, 2]. I then substituted this result along with the matrix for 2I into the full expression. After computation, the final result turned out to be the zero matrix, confirming that A² − 5A − 2I = 0.
Kindly see the step-by-step workings below;

Thank you for visiting my blog, and I hope you found this explanation both insightful and educative.

Tools Used

Graphics tablet/Pen
Miro online white board
Laptop

Video edited with VSDC

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