Search & Filtering
Let A=[a b c ←Matrix
d e f
g h i]
where a, b, c, d,e, f, g, h, i are some real numbers, if det(A)=5 answer the following questions:
- Is A invertible? (Justify your answer). Find rank(A)
- Let b= [a+d b+e c+f ←Matrix
d e f
2g 2h 2i]
And, C= [a b c ←Matrix
-2d -2e -2f
3g 3h 3I ]
Compute det(B) and det(C).
(C) Compute det(A^-1) and det(adj(A)).
<e> Show that if P and Q are vector Subspaces of a vector space V then P ∩ Q is also a vector subspace of V.
Find the general solution of the linear system
whose augmented matrix is
0 1 1 1
1 3 5 0
.
Write the vector (1, −2, 5) as a linear combination of the vectors (1, 1, 1),(1, 2, 3)
and (2, −1, 1)
Consider the following systemof linear equations:
x+2y+2z=1,x+ay+3z=3,x+11y+az=b.
For which values of a does the system have a unique solution. and for which pairs of values (a,b) does the system have more than on solution?
Given that M is a singular matrix, evaluate x where;
6 7 -1
M = 3 x 5
9 11 x
The inter-industry flow of the products of three industries is given below:
Production Sector Consumption Sector Domestic
Demand
Total Output
X Y Z
X 45 12 10 83 150
Y 30 48 10 32 120
Z 45 12 30 13 100
Labour Hours 75 48 20
(a) Determine the input-output matrix and test Hawkins- Simon conditions for the
viability of the system.
(b) If the domestic demand changes to 90,40 and 30 units respectively, what should
be the gross output of each sector in order to meet the demands.
(c) If the total labour available if 180 hours, is the solution feasible?
(d) Find the equilibrium prices if the wage rate is Rs.200.
(a) Consider the following system of equations:
x + 3y + 5z = b1
2x + 4y + 6z = b2.
Show that there are infinitely many solutions no matter the values of b1 and b2.
A. Use the linear function in the table below to answer the question.
x.. 5 , 10 , 15 , 20, 25 , 30
y.. -6 , -6 , -6 , -6 , -6 , -6
Which statement about the function in the table and the line represented by y=6
y=6 is true
a. The lines both cross the x−axis but not the y−axis.
b. The lines both cross through the origin
c. The lines do not intersect
d. The lines have the same y−intercept
For p∈P3(R) given by p(x)=a0+a1x+⋯+a3x3, let s(p)=a0+a1+a2+a3 and det(p)=a0. Also, corresponding to the polynomial p∈P3(R), we define the polynomial p∗ to be p(−x). Which of the following are subspaces of P3(R) ?
#340153 on Dec 2023