linear algebra i want detailed steps please do parts adSolut

linear algebra, i want detailed steps please
do parts a-d

Solution

With this alternative notation d dx + 2 a b c B0 = d dx + 2 (a + bx + cx2 ) = (b + 2cx) + (2a + 2bx + 2cx2 ) = (2a + b) + (2b + 2c)x + 2cx2 = 2a + b 2b + 2c 2c B0 = 2 1 0 0 2 2 0 0 2 a b c B0 . Notice that we have obtained a different matrix for the same linear function. The equation we started with d dx + 2 f = x + 1 2 1 0 0 2 2 0 0 2 a b c B0 = 1 1 0 B0 2a + b = 1 2b + 2c = 1 2c = 0