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Let R2x2 be a linear space with all 2 × 2 real matrices. (1) Find a basis of R22 and dim (R²x2); (2) Find the coordinate of the matrix 1 -2 0 3 under your given basis in (1); (3) If the inner-product on R2x2 is defined by (A, B) = tr(BT A), VA, BER²X2 find an orthonormal basis of R²×2 using the Gram-Schmidt process.

Let R2x2 be a linear space with all 2 × 2 real matrices. (1) Find a basis of R22 and dim (R²x2); (2) Find the coordinate of the matrix 1 -2 0 3 under your given basis in (1); (3) If the inner-product on R2x2 is defined by (A, B) = tr(BT A), VA, BER²X2 find an orthonormal basis of R²×2 using the Gram-Schmidt process.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Let R2x2 be a linear space with all 2 × 2 real matrices. (1) Find a basis of R2x2 and dim (R²×2); (2) Find the coordinate of the matrix 1 -2 3 under your given basis in (1); (3) If the inner-product on R2x2 is defined by (A,B) = tr(BT A), VA, BER²X2 find an orthonormal basis of R2X2 using the Gram-Schmidt process.
Transcribed Image Text:Let R2x2 be a linear space with all 2 × 2 real matrices. (1) Find a basis of R2x2 and dim (R²×2); (2) Find the coordinate of the matrix 1 -2 3 under your given basis in (1); (3) If the inner-product on R2x2 is defined by (A,B) = tr(BT A), VA, BER²X2 find an orthonormal basis of R2X2 using the Gram-Schmidt process.
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