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In this lesson, we will learn how to use the matrix multiplication to determine the square and cube of a square matrix.
Q1:
Given that the eigenvalues of the nondefective 𝑛 × 𝑛 matrix 𝐴 are 1 and − 1 , find 𝐴 1 2 .
Q2:
Find ⎛ ⎜ ⎜ ⎝ 3 2 1 − 1 2 0 ⎞ ⎟ ⎟ ⎠ 3 5 and l i m 𝑛 → ∞ 𝑛 ⎛ ⎜ ⎜ ⎝ 3 2 1 − 1 2 0 ⎞ ⎟ ⎟ ⎠ .
Q3:
Given that 𝑂 is a 3 × 3 zero matrix, find 𝑂 .
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