if the last row of a matrix has no leading entries, why does is it linearly...
8. Let A be a 5 x 4 matrix such that its reduced row echelon form has 4 pivot positions (leading entries). Which of the following statements is TRUE? a) The linear transformation T : R4 → R5 defined by T(X) = AX is onto. b) AX = 0 has a unique solution. c) Columns of A are linearly dependent. d) AX b is consistent for every vector b in R
The reduced row echelon form of a singular matrix has a row of zeros. Select one: True False Subsets of linearly independent sets are linearly independent. Select one: True False
Explain why S is not a basis for M2,2 s-1 1 S is linearly dependent S does not span M2,2 S is linearly dependent and does not span M2,2 Explain why S is not a basis for M2,2 s-1 1 S is linearly dependent S does not span M2,2 S is linearly dependent and does not span M2,2
Explain why the columns of an nxn matrix A are linearly independent when A is invertible Choose the correct answer below. O A. IFA is invertible, then for all x there is a b such that Ax=b. Since x = 0 is a solution of Ax0, the columns of A must be linearly independent OB. IA is invertible, then A has an inverse matrix A Since AA A AA must have linearly independent columns O C. If A is invertible,...
747-38 1026 59% webwork.math.mcgill.ca Problem 5 linearly dependent linearly dependent At least one of the answers above is NOT correct. 15 o to O- 40 (1 point) Let Problem 6 Problem 7 Problem 8 Problem 9 Problem 10 Problem 11 Problem 12 Problem 13 Problem 14 Problem 15 Problem 16 Problem 17 15 B = 12 1-6 -9 -4 3 -101 -8 4 ] (a) Find the reduced row echelon form of the matrix B mref(B) = (b) How many...
Please be clear. 2. Prove that the columns of a matrix A are linearly independent if and only if Ax = 0 has only the trivial solution. 3. Prove that any set of p vectors in R™ is linearly dependent if p > n.
Perform the following matrix operation. Enter your matrix by row, with entries separated by commas. would be entered as a,b,c,d. 49cdan Do not round your answers. st Save Submit Problem #4 for Grading Attempt #1 | Attempt #2 Attempt #3 Problem #4 Your Answer: Your Mark: Perform the following matrix operation. [1 212 2:] Enter your matrix by row, with entries separated by commas. uld be entered as a,b,c,d,e,f
3. Explain why the determinant of a matrix that is row equivalent to the identity matrix In is nonzero.
say we have a matrix like this with an all zero row at the bottom. Why is it that we will have infinitely many solutions? also if the constant in the last row was a not zero then there would be no solutions right? thanks for the help - 2. w W 2 0 0 0 00 0
(a). Determine whether the set is linearly dependent or independent. Further, if it is linearly dependent, express one of the polynomials as a linear combination of others. (b). Determine whether the set can be considered as a basis of the vector space P2, which is the set of all polynomials of degree not more than 2 under addition and scalar multiplication. (1). B = {1 – 2,1 – 22, x – x2} (Hint: Similar to the matrix case in last...