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 matrix1 -23under your given basis in (1);(3) If the inner-product on R2x2 is defined by(A,B) = tr(BT A), VA, BER²X2find an orthonormal basis of R2X2 using the Gram-Schmidt process.

Given be a linear space with all real matrices.Therefore .We need to find the basis of .The inner…

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.