Express the image of the matrixA =1 1 1 6 1 2 3 4 1 3 5 2 1 4 7 0as the kernel of a
Chapter 3, Problem 42(choose chapter or problem)
Express the image of the matrixA =1 1 1 6 1 2 3 4 1 3 5 2 1 4 7 0as the kernel of a matrix B. Hint: The image of A consists of all vectors y in R4 such that the system Ax = y is consistent. Write this system more explicitly:*1 + x2 4- *3 + 6 jc4 = y i *1 -|- 2X2 + 3*3 + 4*4 = V2 *1 -I- 3*2 4* 5*3 + 2*4 = *1 4- 4*2 + 7*3 =>3y4Now, reduce rows:*1 - *3 + 8*4 = 4v3 - 3^4 *2 -f- 2*3 - 2*4 = - V3 -I- >4 o = Vl - 3>3 4- 2.V4 0 = y2 2y3 4" J4For which vectors y is this system consistent? The answer allows you to express im(A) as the kernel of a 2 x 4 matrix B.
Unfortunately, we don't have that question answered yet. But you can get it answered in just 5 hours by Logging in or Becoming a subscriber.
Becoming a subscriber
Or look for another answer