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Linear Algebra
Find a basis and the dimension of the subspace w of V spanned by the matrices
A=[ 1 2
-1 3]
B=[ 2 5
1 -1]
C=[3 4
-2 5]
A=[ 1 2
-1 3]
B=[ 2 5
1 -1]
C=[3 4
-2 5]
Linear Algebra
Determine whether or not the following vectors span R^3
u1 = ( 1, 1, 2), u2 = ( 1, -1, 2 ) and u3 = ( 1, 0, 1 ).
u1 = ( 1, 1, 2), u2 = ( 1, -1, 2 ) and u3 = ( 1, 0, 1 ).
Linear Algebra
Determine the polynomial function whose graph passes through the points (2, 4), (3,6) and (5,10). Also sketch the graph of the polynomial function. (Using Cramer’s Method).
Linear Algebra
Let T: R^2 to R^3 be defined by (a, b)=(a+b, a-2b, 3a+b). Show that T is nonsingular. Hence find T inverse.
Linear Algebra
Find a linear mapping T: R^3 tends to R^3, whose image is spanned by (1, 2, 3),
(4, 5, 6)
(4, 5, 6)
Linear Algebra
Show that
Rank(ST)=Rank s ,if T is non singular
Where S,T : V->V are linear transformation of a finite dimensional vector space.
Rank(ST)=Rank s ,if T is non singular
Where S,T : V->V are linear transformation of a finite dimensional vector space.
Linear Algebra
Given the homogeneous system of linear equations:
x1 + 2x2 − 2x3 + 2x4 − x5 = 0
x1 + 2x2 − x3 + 3x4 − 2x5 = 0
2x1 + 4x2 − 7x3 + x4 + x5 = 0
4.1. Write out the augmented matrix for the system of equations.
2.2. Solve the system by Gauss elimination method to the augmented matrix and determine a basis and the dimension of the solution space S of the homogeneous system.
.
Linear Algebra
Let W = {(a, b, c): a = b + c , a, b , c ∈ ℝ}. Show whether W is a subspace of ℝ3
.
.
Linear Algebra
Find all the roots in C of the equation x^4-2x^3+4x^2+6x-21=0, give n that two of its roots are equal in magnitude and opposite in sign.
Linear Algebra
Let T be a linear operator whose matrix with
respect to the basis {(1,1,1),(1,-1,0),(1,0,-1)} is the matrix [
4 0 0
0 1 0
0 0 1. ]
Obtain the matrix of T wrt the standard basis.
respect to the basis {(1,1,1),(1,-1,0),(1,0,-1)} is the matrix [
4 0 0
0 1 0
0 0 1. ]
Obtain the matrix of T wrt the standard basis.
