G Are the following statements true or false? 1. Any linear combination of vectors can always be written in the form Ax for a suitable matrix A and vector x.

The statement is true that any linear combination of vectors can always be written in the form Ax for suitable matrix A and vector x.

Step-by-step explanation:

Let

a1x1 + a2x2 + a3x3 + ... + anxn = d1

b1x1 + b2x2 + b3x3 + ... + bnxn = d2

.

.

.

c1x1 + c2x2 + c3x3 + ... + cnxn = dn

be a linear system, and let

[a1 a2 a3 ... an][x1] = [d1]

[b1 b2 b3 ... bn][x2] [d2]

[. . . .

[. . . .

[. . . .

[c1 c2 c3 ... cn][xn] [dn]

be the augmented matrix of the linear system. The augmented matrix can be represented as Ax = d

Where A is the matrix of (a1, a2,, an), x is (x1, x2, x3, ..., xn), and d = (d1, d2, d3,..., dn) .

The solution set to the linear system is the same as the solution set of Ax = d.

a

step-by-step explanation:

b: |12 – x| ≤ 0.25

step-by-step explanation:      

let x be the possible lengths in inches, of the ribbons jaime cut.

we have been given that jaime is cutting strips of ribbon for a project. he tries to cut each piece to be 12 inches long, but sometimes he cuts it too long or too short by as much as 0.25 inch.  

we can represent this information in an inequality as:

by the definition of absolute value function we will get,

upon combining our inequalities we will get,

therefore, the inequality   describes all the possible lengths (x), in inches, of the ribbons jaime cut.

step-by-step explanation: