Ex 4.1 | Q : 4 | CH : 4 | Matrices & Determinants | 1st Year Math | New PTB 2025 #11thclassmath
In this video, we solve Exercise 4.1 Question 4 from Chapter 4: Matrices and Determinants of the 1st Year Mathematics (New PTB 2025). We are given a 3x4 matrix A, and the task is to compute: AA′ (A multiplied by its transpose) A′A (Transpose multiplied by original matrix) ((A′)′) (Transpose of transpose of A) This topic is essential for understanding the properties of matrices and transposes in linear algebra. ✅ Ideal for students preparing for board exams and following the Punjab Textbook Board (PTB) curriculum. 🎓 Learn step-by-step matrix multiplication and transpose operations. 📌 Topics Covered: Matrix multiplication Transpose rules Square matrices Application of matrix operations 🔔 Subscribe to "Learn with Khuram" for more videos from Chapter 4 Matrices and other exercises from Class 11 Math New Book (2025) 1st Year Students FSC Pre-Engineering Punjab Board PTB 2025 Matrices & Determinants Revision Board Exam Preparation 🔔 Subscribe to Learn with Khuram for more math lessons! #learnwithkhuram Chapter 4 Matrices and Determinants Exercise 4.1 Ex 4.1 Q1 Ex 4.1 Question 1 Matrices Exercise 4.1 Determinants Exercise 4.1 PTB Math Chapter 4 1st year math exercise 4.1 1st year maths matrices Class 11 Chapter 4 Math Matrices 1st year Matrices 11th class Matrix multiplication class 11 Matrix identity property IA = A matrix Matrix multiplication example Matrix proof class 11 Matrix exercise solutions Matrix properties class 11 Matrices identity property Identity matrix multiplication Matrix multiplication with identity Matrix multiplication rules Matrix class 11 full explanation Matrix solved question 1 Exercise 4.1 full solution Chapter 4 Exercise 4.1 Q1 solution Matrix by identity matrix Matrix multiplication tricks Matrices class 11 PTB Matrices solution Punjab board Matrices 1st year solved Matrices exercise 4.1 solution 11th class mathematics chapter 4 11th class math matrix topic Chapter 4 solved questions 1st year math full solution New PTB math chapter 4 New 2025 PTB Math Solution Matrix multiplication rules for students Matrix multiplication class 11 Matrix solution with explanation Matrix exercise solved in urdu Matrix for Punjab board Matrix tutorial in urdu Matrix tutorial in hindi Matrix multiplication ka asan tareeqa how to multiply Matrix class 11 ex 4.1 question 1 easy matrix multiplication trick Matrix properties class 11 exercise Matrix solution Urdu Hindi Matrix solution Punjab board class 11 PTB math chapter 4 identity matrix 1st year math chapter 4 solved in urdu learn matrix multiplication fast identity matrix multiplication example matrix multiplication ka short trick how to multiply 3x4 matrix with I3 what happens when you multiply matrix by identity identity matrix rule proof matrix multiplication tutorial class 11 matrix multiplication urdu Punjab textbook board math solution 1st year chapter 4 explanation class 11 math chapter 4 full Ex 4.1 Q1 matrix identity rule Matrix solved questions for board Matrix multiplication step by step Matrix A times I = A identity matrix 3x3 and 4x4 multiplication matrix proof IA = A matrix proof AI = A Matrix properties with examples Matrix A = I3 * A proof Matrix A = A * I4 proof matrix examples class 11 PTB class 11 math exercise 4.1 guide matrix identity multiplication guide chapter 4 matrix full explanation Matrix IA = A proof urdu Matrix AI = A proof urdu #11thclassmath #matrices #determinants #exercise4_1 #identitymatrix #matrixmultiplication #mathptb2025 #chapter4 #class11math #matrixproof #learnwithkhuram #mathsolutions #punjabtextbookboard #urdulectures #matrixurdu #matrixtricks #matrixproperties #class11chapter4 Exercise 4.1, Question 1 (i & ii) Matrices and Determinants 1st Year Math Punjab Textbook Board (PTB) 2025 #11thClassMath #1stYearMath #Chapter4 #Exercise4_1 #Matrices #Determinants #MatrixMultiplication #IdentityMatrix #MatrixProof #MathSolution #MathLecture #Class11Math #MathForBeginners #MathTutorial #MathTricks #MatrixConcepts #MatrixAlgebra #MathPunjabBoard #MathPTB2025 #MathWithKhuram #UrduMath #UrduLectures #MathInUrdu #PunjabTextbookBoard #PTBMath #PTB2025 #UrduMedium #FScMath #FScPart1 #FirstYearMath #1stYearScience #1stYearStudy #MatricToFSc #PakistaniStudents #CollegeMath #MathUrduMedium #MathExplained #MathematicsClass11 #LearnInUrdu #MathUrduGuide #MatrixExamples #MatrixBasics #MatrixRules #MatrixIdentity #MatrixByIdentity #MatrixProofs #MatrixOperations #MatrixIAEqualsA #MatrixAIEqualsA #Matrix3x4 #IdentityMatrixMultiplication #MatrixExplanation #MatrixMultiplicationRules #MatrixProperties #MatrixSizeCompatibility #MatrixIntroduction #MatrixBoardExam #MatrixUnderstanding #MatrixClassLecture #MatrixFunction #MathAcademy #StudyWithMe #LearnWithKhuram #YouTubeLearning #EduContent #PakistanEducation #AcademicSupport #OnlineLearning #YouTubeClassroom #Easymath #MathMadeSimple #CollegePrep #MathematicsFun #MathBoardPapers #TextbookMath #NewSyllabus2025 #PunjabBoardMath #HighSchoolMath #CollegeEntranceMath #MathForAll
