Linear Algebra Answers

Show that if be the Eigenvalues of the matrix, then has the Eigenvalues

.

λ1, λ2, λ3, . . . λn A An

λn

1 , λ n

2 , λn

3 . . . λn

n

Find the inverse of the given set of ordered pairs, Then, type F if the inverse is a function or R if its is a mere relation.

1.) {(-3,5), (2,-4), (6,10), (3,-5)}

2.) {(5,1), (4,2), (3,3), (2,5)}

3.) {(1,1), (2,2), (3,3), (4,4)}

Show that if be the Eigenvalues of the matrix, then has the Eigenvalues

.

λ1, λ2, λ3, . . . λn A An

λn

1 , λ n

2 , λn

3 . . . λn

n

In R

4

let L

1

​

be the subspace spaned by the vectors a=(1;2;5;1), b=(4;3;3;0), c=(7;4;1;−1), and let L

2

​

be the subspace spaned by the vectors d=(1;1;1;1), f=(−1;0;3;−1) and g=(5;2;−1;−3). Find the dimension of L

1

​

∩L

2

​

.

In R^3 we have a = (1, 0,-2); b = (-1, 3, 1) and we consider x = a + b; y = -2a + b and z =3a – 5b.

Using the properties of the vector space, calculate T = 2x – 3y + z.

Given

"A=\\left(\\begin{array}{rr}-2&2\\\\2&-4\\end{array}\\right)\\quad \\textrm{and} \\quad B=\\left(\\begin{array}{rr}2&3\\\\2&-1\\end{array}\\right)."

Select the option(s) below which represent "\\left(AB^{-1}\\right)^{-1}."

1. "\\displaystyle \\left(\\begin{array}{rr}-3.5&-2.5\\\\-1.5&-0.5\\end{array}\\right)."
2. "\\displaystyle \\left(\\begin{array}{rr}3.5&2.5\\\\1.5&0.5\\end{array}\\right)."
3. A^-1B
4. B^-1A^-1
5. BA^-1