Let A be a 3x3 matrix whose column vectors add up to zero,that is a 1 +a 2 +a 3

Question

Let A be a 3x3 matrix whose column vectors add up to zero,that is a1+a2+a3=0 and letb=2a1-3a2+5a3 (a) is the matrix A nonsingular? Explain. (b) will the system Ax=b be consistant? How many solutionswill the system have? Explain. (problem is not in a book) Let A be a 3x3 matrix whose column vectors add up to zero,that is a1+a2+a3=0 and letb=2a1-3a2+5a3 (a) is the matrix A nonsingular? Explain. (b) will the system Ax=b be consistant? How many solutionswill the system have? Explain. (problem is not in a book) (a) is the matrix A nonsingular? Explain. (b) will the system Ax=b be consistant? How many solutionswill the system have? Explain. (problem is not in a book)

Explanation / Answer

Its late so sorry if I misunderstood your problem. A) Of course the matrix A is non singular! This just means A is invertible, and we know it is since we can solve Ax=b (invertibility is needed because to solve for x we need A^-1 * A * x = A^-1 * b or x = A^-1 * b) And why do we know we can solve Ax = b? Look at b = 2aw -3a2 + 5a3. b is a combination of the columns (ie its in the column space). B) The system will be consistent for the reasons given in A. Moreover, an n by n matrix with n pivots will yield one single solution to Ax=b. Cheers!

Related Questions

Navigate

• Browse (All)
• Browse L
• Subjects

---

---

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