Quadratic Forms
Curriculum and historical examination lineage for Quadratic Forms under Unit 1 (Matrices and Linear Algebra) of Calculus And Linear Algebra (21MAB101T) at SRMIST.
Historical appearance distribution across SRMIST Formative Tests (CT1, CT2) and University End Semester examinations.
Factual marks weightage of questions asked on this topic in historical examinations.
Question templates that recur across multiple examination cycles with similar conceptual stems.
“Reduce the Quadratic form $x^2 + y^2 + z^2 - 2xy - 2yz - 2zx$ to canonical form by orthogonal...”
“The quadratic form x^2 + y^2 + z^2 is (A) Positive definite (B) Negative definite (C) Indefinite...”
“Reduce the Quadratic form \(3x_1^2 - 3x_2^2 - 5x_3^2 - 2x_1x_2 - 6x_2x_3 - 6x_3x_1\) to the...”
“Determine the nature of the Quadratic form $x_1^2 + 3x_2^2 + 6x_3^2 + 2x_1x_2 + 2x_2x_3 + 4x_3x_1$...”
“Discuss the nature of the Quadratic form \(x_1^2 + 2x_2^2 + 3x_3^2 + 2x_2x_3 - 2x_1x_3 + 2x_2x_1\),...”
Representative historical questions extracted directly from SRMIST examination papers.
Reduce the Quadratic form \(3x_1^2 - 3x_2^2 - 5x_3^2 - 2x_1x_2 - 6x_2x_3 - 6x_3x_1\) to the Canonical form by an orthogonal transformation and find its rank, index, signature,...
Determine the nature of the Quadratic form $x_1^2 + 3x_2^2 + 6x_3^2 + 2x_1x_2 + 2x_2x_3 + 4x_3x_1$ without reducing it to the canonical form.
Reduce the Quadratic form $x^2 + y^2 + z^2 - 2xy - 2yz - 2zx$ to canonical form by orthogonal reduction. Hence find the rank, index and signature of the Quadratic form.
Discuss the nature of the Quadratic form \(x_1^2 + 2x_2^2 + 3x_3^2 + 2x_2x_3 - 2x_1x_3 + 2x_2x_1\), without reducing to canonical form. [4]
Find the eigenvalues and nature of the quadratic form.
Examinations where questions for Quadratic Forms have appeared.
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