1. MATRIXALGEBRA

2. A systematic approach of theelimination method for solving asystem of linear equations providesanother method of solution thatinvolves a simplified notation.3 ways in finding determinants:Criss-cross multiplicationRowColumn 3. DETERMINING THE ERROR OF 3X3 MATRIX 4. The Given Matrix:3 1 1A=2 -4 -37 -2 0 5. 3 1 1 3 1 2 -4 -3 2 -4 7 -2 07 -2 (0 -21 -4) - (-28 +18+0 ) = -15Criss-cross multiplication 6. Cofactor: 3= -4 -3-20 = -6 1= 2-370= 21 1= 2 -47 -2= 24 7. Cofactor:2= 11 -2 0=2-4= 3 17 0= -7-3= 317 -2 = -13 8. Cofactor: 7= 1 1-4 -3=1 -2= 31 2 -3 = -11 0= 3 12 -4 = -14 9. Inverse Matrix:A-1 = -1/15 -6 2 1 +- + 21 -7 -11 -+ - 24 -13 -14+- + 6/15 2/15 -1/15A-1 =21/15 7/15 -11/15-24/15 -13/15 14/15 10. Identity Matrix31 1 6/15 2/15 -1/15AA-1= 2 -4 -3 21/15 7/15 -11/157 -20 -24/15 -13/15 14/15 1 0 0=0 1 0 0 0 1 11. Remember: The first thing we should do is to identify thecorrect determinant and finding the inverseand identity of the matrix given was done inorder to prove whether the determinant usedwasnt wrong. 12. ERRORSCriss-Cross MultiplicationRow DeterminantColumn Determinant 13. Criss-Cross 31 131 2 -4 -3 24 7 -20 7-2 = -21 - 4 + 28 18 = -15 14. Criss-Cross7 -207 -231 1 312 -4 -32 -4= -21 - 4 + 28 18= -15 15. Criss-Cross 7 -207 -2 2 -4 -32 -4 31131 = -28 + 18 + 21 + 4 = 15 ERROR 16. Criss-Cross31 1 317 -207 -22 -4 -32 -4= 18 - 28 + 4 + 21= 15 ERROR 17. Criss-Cross2 -4 -32 -431 1 317 -207 -2= -28 +18 + 21 4= 15 ERROR 18. Criss-Cross2 -4 -3247 -207 -231 1 31= -4 - 21 - 18 + 28= -15 19. Column 31 1 2 -4 -3 7 -20 = 1(24) + 3(-13) + 0 = -15 = 1(21) + 4(-7) - 2(-11) = 15 ERROR = 3(-6) 2(2) + 7(1) = -15 20. Column 31 1 7 -20 2 -4 -3 = 1(-24) 0 3(-13) = 15 ERROR = 1(-21) + 2(-11) - 4(-7) = -15 = 3(6) 7(1) + 2(2) = 15 ERROR 21. ROW31 12 -4 -37 -20 = 7(1) + 2(-11) + 0(-14) = -15 = 2(2) + 4(-7) - 3(-13) = 15 ERROR = 3(-6) 1(21) + 1(24) = -15 22. ROW31 17 -202 -4 -3 = 2(2) + 4(-7) 3(-13) = 15 ERROR = 7(1) + 2(-11) - O(-14) = -15 = 3(6) 1(-21) + 1(-24) = 15 ERROR 23. Tip in finding the error:If the determinant youve found using criss-cross multiplication in matrix given is correct, the error in row and column was found in the middle row and column but if the determinant youve found using criss-cross multiplication in the given matrix is the error, the error in row and column was found in the first and last row and column.