Please give examples of matrices which
(1) is of size 2 × 4, in row echelon...
Please give examples of matrices which
(1) is of size 2 × 4, in row echelon form but not reduced row
echelon form, with exactly 6 zero entries.
(2) is of size 5 × 3, in reduced row echelon form with exactly
one zero row.
If A=[(1, 2,1)
(2, 0, 0)
(0, 5, 0)]
A: R3->R3
1) Find the row reduced...
If A=[(1, 2,1)
(2, 0, 0)
(0, 5, 0)]
A: R3->R3
1) Find the row reduced echelon form of A
2) Find the image of A
3) Find a nonzero vector in ker(A)
2X1-X2+X3+7X4=0
-1X1-2X2-3X3-11X4=0
-1X1+4X2+3X3+7X4=0
a. Find the reduced row - echelon form of the coefficient
matrix
b....
2X1-X2+X3+7X4=0
-1X1-2X2-3X3-11X4=0
-1X1+4X2+3X3+7X4=0
a. Find the reduced row - echelon form of the coefficient
matrix
b. State the solutions for variables X1,X2,X3,X4 (including
parameters s and t)
c. Find two solution vectors u and v such that the solution
space is \
a set of all linear combinations of the form su + tv.
1. Let a,b,c,d be row vectors and form the matrix A whose rows
are a,b,c,d. If...
1. Let a,b,c,d be row vectors and form the matrix A whose rows
are a,b,c,d. If by a sequence of row operations applied to A we
reach a matrix whose last row is 0 (all entries are 0) then:
a. a,b,c,d are linearly dependent
b. one of a,b,c,d must be 0.
c. {a,b,c,d} is linearly independent.
d. {a,b,c,d} is a basis.
2. Suppose a, b, c, d are vectors in R4 . Then they form a...
1. Let v1,…,vn be a basis of a vector space V. Show that
(a) for any...
1. Let v1,…,vn be a basis of a vector space V. Show that
(a) for any non-zero λ1,…,λn∈R, λ1v1,…,λnvn is also a basis of
V.
(b) Let ui=v1+⋯+vi, 1≤i≤n. Show that u1,…,un is a basis of
V.