Let A be the following 4x6 matrix and suppose A is row equivalent to the matrix

ID: 2984723 • Letter: L

Question

Let A be the following 4x6 matrix and suppose A is row equivalent to the matrix in reduced row echelon form as presented

(sorry i have not figured out how to put matrices in.)

A=Row 1: 1, 1, -1, 1, -1, -1 A is rowequivalent row 1: 1, 0, 2, 0, 0, 1

Row 2: 1, -1, 5, -3, 2, 0 to reduced row row 2: 0, 1, -3, 0, 0, -1

Row 3: 1, 1, -1, 4, -3, 1 echelon forme row 3: 0, 0, 0, 1, 0, 4

Row 4: -3, 4, -18, -2,2,-5 row 4: 0, 0, 0, 0, 1, 5

Let W be the row space of A

Find all values of a and b so that (5, 4, a, 2, 1, b) is in W or explain why a and b do not exist.

Rows in reduced echelon form are

[1, 0, 2, 0, 0, 1]

[0, 1, -3, 0, 0, -1]

[0, 0, 0, 1, 0, 4]

[0, 0, 0, 0, 1, 5]

The curcial point to observe is that row space of the matrix,W is same as row space of its row reduced echelon form.

W = Row space of reduced echelon form is

{x[1, 0, 2, 0, 0, 1]+y[0, 1, -3, 0, 0, -1]+z[0, 0, 0, 1, 0, 4]+w[0, 0, 0, 0, 1, 5]:

x,y,z,w are reals}

[5, 4, a, 2, 1, b] is in W

=> x = 5,looking at first coordinate,

y = 4,second coordinate,z=2,looking at fourth coordinate

w=1,fifth coordinate

=>a=2*5-3*4 = -2 and b = 5-4+4*2+5*1 = 14

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