# Algebra Questions: Matrices and Determinants

## Transcribed Text

1. Consider the matrices 4- 3 6 0 2 3 C - 2 2 3 1) 4 0 1 2 -3 - 0 A - 0 I 0 0 Calculate, where possible: (a) 3A, (b)B-C, (c)-3D-2E, (d) CD, (e) DC, (f) CCT. 2. Give an example of two 2x2 matrices Xand Y such that XY 6= YX. 3. Give an example of two 2x2 matrices Xand Y such that XY=0, but the entries of X and Y are all non- zero. F = 3 1 -2 4. Find the determinant and the inverse of the following matrix: G - I 5. Let Find a general expression for G". Hint: Calculate G, G2,G³, and look for a pattern.

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