Solving Mathematical Problems Involving Matrices

Matrices Assignment
Student’s Name
Institution
Course
Professor’s name
Date
Part 1
A = -2053 B = 024-6
1 2B = 2 024-6
= 048-12
2 5B = 5 024-6
= 01020-30
3 -3A = -3 -2053
= 60-15-9
4 -4B + 5A
-4B = -4 024-6 = 0-8-1624
5A = 5 -2053 = -1002515
Therefore,
-4B + 5A = 0-8-1624 + -1002515
= -10-8939
5 3B - 10A
3B = 3024-6 = 0612-18
10A = 10 -2053 = -2005030
Therefore,
3B - 10A = 0612-18 - -2005030
= 206-38-48
Part 2
Matrix Products
Q9. 1234-13
= (1 x-1) + (2x3)(3 x-1) + (4x3) = -1+ 6-3+12
= 59
Q11. 22-15010-2-1502
= (0+-2+0)-4+10+-20+0+0(-10+0+2
= -240-8
Q12. -9313002-14
= (-18+ -3+46+0+0
= -176
Determine whether the following matrices are inverse of each other by computing their product
Q27. 523-1 -123-4
= (-5+6)(10+-8)-3+ -36+4
= 12-610
Matrix B is the inverse of A if BA = I and AB = I
Therefore, 523-1 and -123-4 are not inverse of each other since their product is not an Identity matrix.
Q32. 254143132 121-5827-11-3
= (2+ -25+284+40+ -442+10+ -121+ -20+212+32-331+8+ -91+ -15+142+24-221+6-6
= 500210041
Matrices 254143132 and 121-5827-11-3 are not inverse of each other since their product is not an Identity matrix.
Find the inverse if it exists
Q33. 2-3-12
Let A = 2-3-12
Write the augmented matrix A|I where I is the 2 X 2 Identity matrix and then perform row operation on A|I to get the matrix of the formI|B. B is the inverse of A
A|I = 2-3-12 | 1001
Change the left side of the matrix into a 2x2 identity matrix
= 2-3-12 | 1001
Change -1, the first element in the second row by adding Row 1 to 2(Row 2). Perform, R1 + 2R2 to row 2, row 1 remains unchanged.
= 2-301 | 1012
Change -3, t...