Let S be the set of all column matrices b such that b, b2, b3 R...
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Let S be the set of all column matrices b such that b, b2, b3 R and the system of equations (in real b3 variables) -x + 2y + 5z = b 2x - 4y + 3z=b x - 2y + 2z=b3 has at least one solution. Then, which of the following system(s) (in real variables) has (have) at least one by solution for each b ES? b (A) x+2y+3z=b, 4y + 5z = b and x +2y+ 6z=b3 (B) x+y+3z=b, 5x + 2y + 6z=b and -2x -y - 3z=b3 (C) -x+2y- 5z = b, 2x - 4y + 10z=b and x-2y + 5z = b3 (D) x + 2y + 5z = b, 2x + 3z = b and x + 4y - 5z = b3 Let S be the set of all column matrices b such that b, b2, b3 R and the system of equations (in real b3 variables) -x + 2y + 5z = b 2x - 4y + 3z=b x - 2y + 2z=b3 has at least one solution. Then, which of the following system(s) (in real variables) has (have) at least one by solution for each b ES? b (A) x+2y+3z=b, 4y + 5z = b and x +2y+ 6z=b3 (B) x+y+3z=b, 5x + 2y + 6z=b and -2x -y - 3z=b3 (C) -x+2y- 5z = b, 2x - 4y + 10z=b and x-2y + 5z = b3 (D) x + 2y + 5z = b, 2x + 3z = b and x + 4y - 5z = b3
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