1. Calculate the following where possible and state the dimension of the result: 1 + 212 - 313 + 214 - 4xs = 0 21 + 12 + 13 - 204 = 1 (a) 2x1 + 4x2 - 513 + 14 - 615 = 0 321 - 2x2 + 13 - 6.14 = -2 5x1 + 10.2 - 13.13 + 4.ra - 1615 = 0 (e) ri +2 - 203 + 4.r. = 5 6.r1 + 13 - 914 = -2 (b) 2x1 + 2x2 - 3x3 + 14 = 3 521 - 12 + 213 - 8.14 = 3 3x, + 3.r, - 483 - 2r, = 1 (c) State - 1=1 1 + 3.r2 + 213 - CA - 25 = 0 (d) 2x, + 6.2 + 503 + 1 - Is = 0 5x1 + 15x2 + 12rs + 24 - 3rs = 0 2. In the following linear systems, m +12 - 23 = 2 mi + + = 2 i. mi + 202 + 23 = 3 ii. 2x1 + 3x2 + 213 = 5 mi + x2- (a' -5)13 = 2 2.21 + 3.x2 - (a' - 1).23 = a +1 determine the values of a for which the resulting linear system has: (a) No solution (b) A unique solution (c) Infinitely many solutions