Linear Algebra Answers

R is a vector space over C with respect to the usual operation of addition and multiplication. true or false.

let A be a matrix of 3×2 order with real entites. H=A(A^TA)^-1A^T . where A^T is the transpose of the matrix. let I be the identity matrix of the order 3×3. H^2=?

An electronics company produces​ transistors, resistors, and computer chips. Each transistor requires 3 units of​ copper, 1 unit of​ zinc, and 2 units of glass. Each resistor requires 3​, 2​, and 1 units of the three​ materials, and each computer chip requires 2​, 1​, and 2 units of these​ materials, respectively. How many of each product can be made with 1500 units of​ copper, 780 units of​ zinc, and 1110 units of​ glass? Solve this exercise by using the inverse of the coefficient matrix to solve a system of equations.
The company can make
​transistors,
​resistors, and
computer chips.

check that p^(e)andp^(0) are subspace of R[x] if p^(e)={p(x)€R[x]|p(x)=p(-x) and p^(0)={p(x)€R[x]p(x)=-p(-x)

the height of an above ground pool is 3 feet. the pool needs to be drained. as the water drains, the height of the water changes at a rate of -(1)/(2) inch per minute. write and sold and equation to find how many minutes it will take to drain the pool

The profit made by a company when 60 units of its product is sold is R 1 600.00. When 150 units of its products are sold, the profit increases to R 5 200.00. Assuming that the profit function is linear and of the form

⎛ 2 0 1 ⎞
9.Given that A = , ⎜ k 2 3 ⎟ what is the value of k, if A is said to be a singular matrix?
⎝ 2 1 4 ⎠

a.8
b.10
c.7
d.-6





⎛1 2 3⎞
10.let A= ⎜4 5 0⎟ then the cofactor of matrix A is the matrix
⎝2 1 4⎠,

a.

⎛ 20 −16 −6 ⎞
A = ⎜−5 −2 3 ⎟
⎝−13 12 −41 ⎠

b.
⎛ 20 −16 −6 ⎞
A = ⎜−5 −2 3 ⎟
⎝−13 12 −3 ⎠

c.
⎛ 20 −16 −6 ⎞
A = ⎜−5 −2 3 ⎟
⎝−15 12 −3 ⎠

d.
⎛ 20 −12 −6 ⎞
A = ⎜−5 −2 3 ⎟
⎝−13 12 −41 ⎠

⎛1 2 3⎞
5. Given that A= ⎜3 2 1⎟ . Find the determinant of A
⎝1 3 2⎠


a.2
b.3
c.1
d.zero

6. A matrix is said to be singular if the determinant is equal to
a.3
b.1
c.zero
d.2

3. A necessary and sufficient condition for a matrix (square) A to be invertible is that
a.A is not equal zero
b.|A|≠0
c.|A|>0
d.A<0

4. Given that x + 2y + 3z =1, 3x + 2y + z = 4, x + 3y + 2z = 0. What is x,y and z?
a.(7/4,-3/4,1/4)
b.(5/4,-2/4,1/4)
c.(1,-3/4,1/4)
d.(1,-2,3)

1.Given that x + 2y = 3, 3x + 4y =1. What is x and y?
a.(1,-1)
b.(2,-2)
c.(-5,4)
d.(4,-5)

2.Given that
(1 3)
(k 4)
is singular matrix. Find the value of k
a.(4/3)
b.(3/5)
c.(3/4)
d.(5/3)