Multiplying a linear equation through by zero is an acceptable elementary row operation. True or false

Find all solutions to the following system of linear equations: 1x1 + 2x2 + -2x3 Ox5 -1 2x1 5x2 + -3x3 -2x5 1 %3D -lx1 + -1x2 + 4x3 + -3x5 6 0x1 + 1x2 + 1x3 + -2x5 3 Note: if you see, for instance, + - 2 in the above system, then this simplifies to -2. Moreover, 1xı is just X1, etc. +s |+t If there is only one free variable, let it be associated to the parameter s and write -99 as the entries of the last vector. Do not leave the entries of that last vector empty. Il ||

Find conditions (i.e., linear equations) on b1, b2, b3 and b4 that make the following system consistent. Show your work. b1 b2 b3 1 5 -2 3 1 8 6 -1 3 -6 b4

Find the set of solutions for the linear system -3x1 6x2 3x3 9. 672 8x3 -8 Use x3, x2, etc. for the free variables if necessary. Indicate if a variable is free by writing the same variable in the space (so if x1 is free, write x1 =x1). 2x2 - x3 - 3 4/3x3 - 4/3 x3 = x3

Determine the values of a for which the following system of linear equations has no solutions, a unique solution, or infinitely many solutions. You can select 'always', 'never', 'a = ', or 'a #', then specify a value or comma-separated list of values. 3x7+6x2+ax3 = 3 2x1+9x2x3 = 17 2x1+7x2-3x3 = 12 No Solutions: Unique Solution: Infinitely Many Solutions: Always Always Always

Write the non-arbitrary parameters in terms of the arbitrary ones.