Saidul Islam RajibMethematics
This is a testinAdvanced matrices and three-dimensional geometry — the algebra of linear systems and the geometry of lines and planes in space, worked the way exams and applications actually use them. ...
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9 lessons · 26 min of reading
Matrices
From matrix algebra and determinants to rank, inverses, and the eigenvalue theory that ties them together.
4 lessons-
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Matrix algebra and special matrices
The operations, the algebra they obey, and the named matrices whose structure does the heavy lifting.
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Determinants and their properties
One number that decides invertibility, scales volume, and turns long computations into short ones when you use its properties.
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The inverse of a matrix
When it exists, two ways to compute it, and why the adjoint method is a proof, not a procedure.
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Rank and solving linear systems
One integer measures how much information a matrix really carries — and decides whether a system has no solution, one, or infinitely many.
Three Dimensional Geometry
Directions, lines and planes in space — the vector machinery that turns spatial questions into short algebra.
5 lessons-
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Direction cosines and direction ratios
How a direction in space is encoded as three numbers, and the one identity that constrains them.
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The straight line in space
A point and a direction fix a line — written as a vector equation, as symmetric Cartesian form, and as parametric coordinates.
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The plane
A point and a normal fix a plane — and the normal vector, read straight from the equation, answers almost every question about it.
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Angles, distances and the line–plane relationship
Every angle and every intersection reduces to a dot product between the right two vectors — once you pick the right two.
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Skew lines, shortest distance and coplanarity
In space, two lines usually neither meet nor run parallel — and one scalar triple product settles the distance between them.