The question listed in the picture Given the following system of equations 3x1 +

Question

The question listed in the picture

Given the following system of equations 3x1 + 5x2 - 4x3 = b1 -3x1 - 2x2 + 4x3 = b2 6x1 + x2 - 8x3 = b3 Write this as matrix equation and identify A, x and b Ax = b Corresponding to matrix A there is a linear transformation T, what is this transformation and this transformation goes from what space to what space. What is the determinant for matrix A and what does this tell you about matrix A being invertible or not? What is a basis for the Null Space of A, what is the rank of the Null Space and what does this tell you about the linear transformation being one-to-one? What is the dimension of the Column Space of A and what does this tell you about the linear transformation being onto or not?

Explanation / Answer

1.

A = [3 5 -4; -3 -2 4;6 1 -8]

b =[b1 b2 b3]'

x= [x1 x2 x3]'

2.

T: R^3-->R^3

such that

T(x) = Ax = (3x1 + 5x2 - 4x3, -3x1 - 2x2 + 4x3, 6x1 + x2 - 8x3 )

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.