Rank-Nullity TheoremThe conservation law relating the image and the kernel of a linear map.MathematicsFor a linear map T from V to W with Vfinite-dimensional, the rank plus the nullity equalsdim V.dim V = rank(T) + nullity(T)A is 3×5 with rank 3Nullity is 25 − 3.T is injectiveNullity is 0Trivial kernel.3×3 matrix of rank 2det(A) = 0So not invertible.THE COMMON MISTAKEReading dim V as the codomain's dimensiondim V is the dimension of the domainRank lives in W and nullity lives in V, but the sum is dim V. Using dim W gives thewrong count whenever the map is not square.Row rank always equals column rank. Rank is the number of pivots, andthat number is the same read either way.Rank-Nullity Theoremlearnposters.com
Rank-Nullity Theorem — printable math wall chart from LearnPosters. Free vector PDF, US Letter and A4.

What’s on the Rank-Nullity Theorem poster

The rule, 3 worked examples, and the mistake everyone makes.

Row rank always equals column rank. Rank is the number of pivots, and that number is the same read either way.

Questions about the Rank-Nullity Theorem poster

What’s on the Rank-Nullity Theorem poster?
The rule, 3 worked examples, and the mistake everyone makes. For a linear map T from V to W with V finite-dimensional, the rank plus the nullity e…; dim V = rank(T) + nullity(T); A is 3×5 with rank 3 = Nullity is 2; T is injective = Nullity is 0; 3×3 matrix of rank 2 = det(A) = 0; Common mistake: Reading dim V as the codomain's dimension → dim V is the dimension of…. Row rank always equals column rank. Rank is the number of pivots, and that number is the same read either way.
Who is the Rank-Nullity Theorem poster for?
Rank-Nullity Theorem belongs to the Mathematics section rather than to a school year, because math is not something one grade owns. Anyone learning linear algebra can pin it up — a beginner, a student mid-course, or someone revising years later.
When should you use the Rank-Nullity Theorem poster?
To get the dimension of a null space without computing it, or to test invertibility. A wall chart earns its place by being glanceable from where the work is happening, so Rank-Nullity Theorem belongs on the wall where that math work actually happens, within glancing distance, rather than filed away.
What other posters go with Rank-Nullity Theorem?
Basis & Dimension, Determinant Properties and Diagonalisation sit alongside Rank-Nullity Theorem in the Mathematics section. Printed together they make a wall rather than a single sheet, which is how a reference set actually gets used.Basis & DimensionDeterminant PropertiesDiagonalisation
Is the Rank-Nullity Theorem poster free to download and print?
Yes. Rank-Nullity Theorem downloads as a free PDF with no account, no email and no watermark, like everything else in the Mathematics section. Print as many copies as you like for a home, a classroom, a library or a tutoring group; reselling the file is the only thing the licence rules out.Read the licence
What size does the Rank-Nullity Theorem poster print at?
Rank-Nullity Theorem is a vector PDF laid out for US Letter, and prints on A4 with Fit to page — the same file, no separate download. Because every mark on it is drawn rather than photographed, it stays sharp enlarged to A3, A2 or A1 at a copy shop. Colour carries emphasis only, so a greyscale print of Rank-Nullity Theorem loses nothing.Printing guide

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