Search & Filtering
1.Which of the following is a linear equation in x,yand z?
1. -x–¹ + e–√²y=3z l, where e= 2.71828
2. 2πln(e–½) - 2y + z= ln(3) - x.
3. √y² + 4y - 2z = 7x.
4.y + 4y - 2z = 7x–².
2.Solve for X from the matrix equation below. Here is the identity matrix and det(A) ≠ 0.
A²X + l = AB
Choose the correct option:
1. X is the identity matrix.
2. X= A–¹B - l
3. X= A–¹B + l
4. X= A–¹B - A
5. X= AB + B
{F} Work Out
1. Solve by crammer's rule, the following equations.
3X + 3Y - Z = 11
2X - Y + 2Z = 9
4X + 3Y - 27 = 25
2. solve the above equations using graphical method.
Determine which of the following is not the solution set of the linear equations below.
3x-y+z=2
2x-z=2
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.
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
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) ?
Find the conical form of a quadratic form Q(x,y)=2x^2+2y^2-2xy by using an orthogonal transformation hence find nature,rank,index and signature of the conical form?
