MH SET 2026 | Linear Algebra April 2024 PYQ 🔥 | Previous Year Paper Discussion

Linear Algebra PYQs from 2020 in Mathematical Science explained with clear concepts and exam-focused approach. Learn dimension of upper triangular matrices, AB and BA determinants, linear systems, rank inequality, null space, projection, singular values, similar matrices, nilpotent and orthogonal matrices for SET and CSIR NET. 🧭 Get Personalized Preparation Guidance: https://ifasonline.com/csir-net/mathe... 🔥Join India's Best Coaching for CSIR NET and GATE Exams: https://ifasonline.com/csir-net/mathe... 📞 Need Guidance? Call/WhatsApp: 9172266888 ━━━━━━━━━━━━━━━━━━━━━━━━━ ⏳ Lecture Timeline: [00:48] Introduction [01:32] Q1: Dimension of 5x5 Complex Upper Triangular Matrices [05:09] Q1 Answer: 30 [05:45] Q2: A is 4x3, B is 3x4, det(AB) [10:17] Q2 Answer: det(AB) = 0 [11:27] Q3: Linear System, 3 Variables, 2 Equations [13:15] No Unique Solution [15:24] Q3 Answer: Infinite Solutions for All b1, b2 [15:30] Q4: Rank of A = 6, Rank of B = 4, Rank of AB [16:43] Rank Inequality [18:43] Q4 Answer: Rank(AB) ≤ 4 [18:53] Q5: Null Space Dimension of Linear Transformation [22:43] Q5 Answer: 2 [22:54] Q6: Projection onto xy-plane [26:01] P² = P [26:37] Q6 Answer: P² = P [27:16] Q7: Singular Values [29:38] Eigenvalues of AᵀA: 7 and 3 [30:36] Q7 Answer: 7 and 3 [30:44] Q8: Properties of Similar Matrices [34:42] Same Trace, Determinant, Char and Minimal Polynomial [35:07] Q8 Answer: All Statements True [35:19] Q9: Nilpotent Matrix A, I + A Invertible [39:13] Eigenvalues of I ± A are 1 [39:57] Q9 Answer: I + A and I - A Invertible [39:57] Q10: Real Orthogonal Matrix, det = -1, det(I - A) [42:39] Example Gives det = 0 [42:46] Q10 Answer: det(I - A) = 0 [44:28] End Of Lecture ━━━━━━━━━━━━━━━━━━━━━━━━━ 📖 Topics Covered in This Lecture: Upper triangular matrix dimension, AB and BA determinants, linear system solutions, rank inequality, null space dimension, projection operator, singular values, similar matrices properties, nilpotent matrix invertibility, orthogonal matrix determinant. ━━━━━━━━━━━━━━━━━━━━━━━━━ 📚 Lecture Summary: In this session, IFAS Expert Faculty solves Linear Algebra PYQs from 2020 for Mathematical Science exams. Questions cover dimension of 5x5 complex upper triangular matrices, determinant of AB and BA for 4x3 and 3x4 matrices, linear system with more variables than equations, rank inequality for 6x7 and 7x5 matrices, null space dimension of linear transformation, projection onto xy-plane, singular values of a matrix, properties of similar matrices, invertibility of I+A and I-A for nilpotent A, and determinant of I-A for real orthogonal 4x4 matrix with det -1. Learn shortcuts, rank-nullity, singular value definition, and exam-focused problem-solving. ━━━━━━━━━━━━━━━━━━━━━━━━━ 🎓 This lecture is highly beneficial for students preparing for: ✅ CSIR NET Mathematical Science ✅ GATE Mathematics ✅ SET Mathematics ✅ TIFR Mathematics ✅ PhD Entrance Exams ━━━━━━━━━━━━━━━━━━━━━━━━━ 🏆 Why IFAS is India’s No. 1 Choice for CSIR NET & GATE Mathematics? (Our Results Speak): ✅ CSIR NET Dec 2025: 4000+ Selections (AIR 3, 8, 9.....) ✅ CSIR NET June 2025: 4200+ Selections (AIR 1, 2, 6, 10...) ✅ CSIR NET Dec 2024: 4000+ Selections (AIR 5, 6, 7, 8, 9...) ✅ CSIR NET June 2024: 2000+ Selections (AIR 3, 10, 13...) ✅ CSIR NET Dec 2023: 1200+ Selections (AIR 2, 4, 5...) 📄 View IFAS Result Sheet: 👉 https://drive.google.com/file/d/1THh6... ━━━━━━━━━━━━━━━━━━━━━━━━━ 🔗 Important Links: 🌍 Visit our Website: https://ifasonline.com 📞 Contact for Queries: 9172266888 ━━━━━━━━━━━━━━━━━━━━━━━━━ 🔗 India's Best Online Classes and Books: 🔥CSIR NET Mathematical Science Live & Recorded Course: https://ifasonline.com/csir-net/mathe... 🎯 GATE Mathematics Recorded Course: https://ifasonline.com/gate/mathemati... 📘CSIR NET Mathematical Science Books: https://ifasonline.com/csir-net/mathe... ━━━━━━━━━━━━━━━━━━━━━━━━━ 📲 Download IFAS App: Android: https://play.google.com/store/apps/de... IOS: https://apps.apple.com/us/app/ifas/id... ━━━━━━━━━━━━━━━━━━━━━━━━━ Stay Updated Via Other Social Media: ✔Telegram: https://t.me/NET_GATE_SET_Maths_Discu... ✔Instagram:   / csir_net_mathematical_science   #csirnetmathematicalscience #gatemathematics #csirnetmaths #csirnetdec2026 #csirnetlecture #ifasmathematics