Its All about Pj Problem Strings - 7 Spaces Of Interest and their associated Basic Sequences; 7 Pj Problems of Interest (PPI) and their Alleles (A)

WiseBites - Chew And Swallow

My Brain Is Stringed - Iremisan Adegiga : I became a TECian (a person or any other being that sees the Universe through the TECTechnics Prism) about two years ago after ... more

Policing The Pursuit Of Knowledge : Policing is the enforcement of the system of laws of a space. The police are ... more

Spiritual But Not Religious - Kimberlee J. Benart : I saw the title of the blog and took the time to read it, but how it saddened me to see it full of harsh unkindness ... more

Mis-Information As A Weapon - The Larger Issue: Information is shared knowledge. The knowledge shared does not have to be accurate...more

I Charlie - A Farmer At Heart: From growing up on a farm in America to pioneering and working in Africa...more

One Nation Under What?: A nation is a group of individuals with different identities... more

Selective Freedom: Freedom is the condition of not being controlled by another. The implication here is not that a person is ... more

Ultimate Reality: the awareness of being establishes reality ... more

Incidental Spying: Spying is incidental if the angle of reflection of the reflection of the incidental ray is zero (the incidental being is masked). When the incidental being is unmasked, the angle of incidence equals the angle of reflection and incidental spying becomes deliberate spying.

All is Mathematics: Nature only speaks mathematics within the context of 7 universal concepts (Pj problems). This language is uniform everywhere in the Universe and is ... more

Good Walls Bad Walls: A wall is a barrier that encloses a space. A wall does not have to be visible to the naked eye. The structure of a wall... more

Spying: spying is covert access into a space of interest in order to obtain data (measurement of observations) and information (shared knowledge). The spy (the entity spying)... more

Mind Warm Ups

The point "." is a mathematical abstraction. It has negligible size and a great sense of position. Consequently, it is front and center in abstract existential reasoning.

A = ((aij)) is a translation matrix of order 3.
aii = 1 for all is; a12 = 0; a13 = x0;
a21 = 0; a23 = y0;
a31 = 0; a32 = 0.
Determine det A. What values of x0 and y0 will cause
every point on the plane to be a fixed point under the translation represented by A.

A = ((aij)) is an orthogonal matrix of order 2.
if a11 = 3/5; a12 = 4/5; a21 = -4/5; a22 = 3/5;
Determine the transpose and inverse of A
and whether A is proper or improper.

A = ((aij)) and B = ((bij)) are matrices
representing projections of the plane.
a11 = 1; a12 = 0; a21 = 0; a22 = 0;
b11 = 1; b12 = 0; a21 = 1; a22 = 0.
Test for the nonsingularity of the transformations.
The point P(1,1) is projected under A, the result is then
projected under B to the point P'.
Determine the coordinates of P'.

A = ((aij)), is the matrix
representing a a shear parallel to the x-axis.
a11 = 1; a12 = k; a21 = m; a22 = n.
A maps the vertices of a rectangle onto the vertices of a parallelogram as follows:
(0,0) -> (0,0); (2,0) -> (2,0);
(2,1) -> (5,1); (0,1) -> (3,1).
Determine the values k, m and n.

A = ((aij)), is a scalar transformation matrix of order 2.
a11 = k; a22 = 1/4.
Determine if A represents a uniform stretching of the plane or a uniform compression of the plane.
What change should be made in A inorder for it to represent a dilation of the plane.
What is the difference between a transformation matrix representing a dilation of the plane
and the transformation matrix representing a magnification of the plane.

The Linear Transformations T1 and T2 are reflections of the plane.
T1 is the case where the points on the x-axis are fixed points.
T2 is the case where the points on the y-axis are fixed points.
Determine the reflection matrix of:
(a)T1 (b)T2

((Aij)) and ((Bij)) are reflection matrices of reflections of the plane.
A11 = 0; A12 = 1; A21 = 1; A22= 0
B11 = 0; B12 = -1; B21 = -1; B22= 0
Determine: (a) The mirror associated with ((Aij))
(b) The mirror associated with ((Bij))

What is the determinant of the rotation matrix of the following transformation:
T(x, y) = (xcosθ - ysinθ, xsinθ + ycosθ).

What is the matrix of the transformation:
T(x, y) = (-x, -y)?

Identitfy the rigid motions that correspond to the following transformations:
(a) T(x, y) = (x+7, y-7).
(b) T1T2(x, y).
Where T1(x, y) = (x, -y) and T2(x, y) = (y, -x).
(c) T(x, y) = (xcosθ - ysinθ, xsinθ + ycosθ).

Abigail asked Abel to work on the transformation
T(x, y) = (x2, xy). Abel computed T and told Abigail he is not interested in T because it corresponds to a non-rigid motion. What is a non-rigid motion? Is Abel right? Describe the non-rigidity of T.

T is an identity transformation. Vector u = (x, y). What is T(u)?

T is a one-to-one linear transformation from the m-dimensional linear space X into the n-dimensional linear space Y. What is the value of m if n2 = 9?

Problems by Peter O. Sagay

Blessed are they that have not seen, and yet have believed. John 20:29