 न्म्॑स्कर आजी आँई कीचना बश्ँवण तो अगग़ रजिख बूभिस्विन दिल आवर्दिनाड रचिट होका देः ऎप इप द़ावे ब्देश पास्कोद्सर कोब स वन क्ला सिक्ल अज़ब्रा आँन्भिन मेट प्रईध , జజ PJ- Allāh-ūdhī Jānātāṁ jānāṁ jānīṁ జజṁ జజ జజ इజ, अदा జజ। జజ జజ ੇ జజ, జజ జజ wherever, జజ జజ జజ, ॢ ॢ ० ी ॰ ॡ ृ ॴ ड़ ४ ॢ । , స pistinc immediately defined krate, what is a determinate, delegate  Olivier                                                                                                                                                                                                                               wła princess Shaun etta ыт  spannend ु ઓ ઉ સ జ ્ �ール �涬 ૂ ઊ ઉ ઒ ં ૂ ઌ ઒ ર ો ખ ઢ એ ૕ �ippy�� સ ઢ ঢ় ે ૕ क ચ ઉ ૙ આ ઍ  give લ ક ব �ī豚 � passions ઀ િ ૈ પ � maritime ੁ ક � 마무� ੍u  COSTA order of a determinant loe the determinant of order two becomes a name so itm determinant consisting two rows and two columns is called requirement of order two for me today I will look at an example so itm determinant it means queand So next, fall of determinant of order 2. Order 2, determinant of order 2, we've called it as a fall. For now, we've determined a1, b1, a2, b2. So for a determinant of value 2, we first multiply a1, b2, that is minus a2, b1. So for a expression, is called the value of the determinant order 2. So, a determinant of value to amy a expression to amy value of the outcome. It amy also known as determinant of order 3. So, determinant of order 3 is a determinant consisting of 3 rows and 3 columns is called a determinant of order 3. So, determinant of order 3 is an example of amy a expression a1, b1, c1, a2, b2, c2, a3, b3, b3, c3. So, a determinant of order 2 amy 3 will come, because a determinant of 3 is called r1, r2, r3. So, a determinant of order 3, a determinant of order 3 is 9 elements. Order 3 determinant not a elements. . . . There are 6 ways to find the value of the determinant, value of the determinant order 3 corresponding to each of the 3 rows r1, r2 and r3 and 3 columns c1, c2 and c3. It amy value of the determinant value of a determinant will am of order 3 along the fast row along the fast row r1. Fast row r1 of the amy value of the determinant of order 3 one will am. So, fast amy value of the determinant, let us consider a determinant of order 3. . . Consider a 1, b 1, c 1, a 2, b 2, c 2, a 3, b 3, c 3. So, amy a determinant of amy expand along row r1. So, fast amy a 1, a 1, j 2, fast row r, fast column column of the set. So, amy a kernel is show minus 1 to the power of 1 plus 1 a 1. So, a element of j 2 row r column to delete, so amy a time b 2, c 2, b 3, c 3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 to the power 3 b1 a2 c3 a3 c2 minus 1 to the power 4 c1 a3 b3 a3 b2 minus 1 over so a1 b2 c3 b3 c2 minus b1 a2 c3 minus a3 c2 c1 a3 b3 minus a3 b2 so if I get problem become a1 b2 c3 a1 b3 c2 minus a2 b1 c3 plus a3 b1 c2 plus a3 b3 c1 so a3 b2 c1 so expression term italic cone so I mean along the first row are CSV an example can explain to you can make me are two are tree my versi one c2 c3 row I mean e derm and concrete determentorva buy I'll show up one so property 1 the value of a determinant remains unchanged if its rows and columns are intersence so this is a determinant of row and columns which I intersence with, so the determinant value remains unchanged so determinant a1, b1, c1, a2, b2, c2, a3, b3, c3 so this is a determinant of row and columns which I intersence with, so I intersence with a1, b1, c1, a2, b2, c3, a3, b3, c3 so I intersence with a row and columns which I intersence with, so the determinant value remains unchanged our we shall mean palm property ii property iii is any 2 rows or columns of a determinant are intersence then sign of the determinant changes 👀 👀 A3, B3, C3 if I do the row 1 or row 2 I will do the inter-sense I will do the mask I will do the minus sign I will do the second row in the first row I will do the first row in the second row so in this case, sign to sandwich the value of the determinant will be here A3, if any two rows or columns of a determinant are identical identical means, all corresponding elements are same then, value of the determinant is 0 so this is equal to the determinant or root of the row or column A k is equal to the determinant or value of the row is 0 so now I will determine A1, B1, C1 A1, B1, C1 A3, B3, C3 so here R1, R2 are identical means they are same they are corresponding elements are same so because this determinant is equal to the value of the row is 0 so this is the property 3 so in this case property 4 is equal to property 4 property 4 is equal to if each element of any row or column is multiplied by a constant such k then the whole determinant get multiplied by k therefore I will determine the first row to k constant is multiplied so this determinant the first row of a protective element is multiplied by k so I will write k into whole determinant because if the row or column or protective element is multiplied by a constant then the determinant is multiplied by k so this is property 4 tarabhi shurami property 5, 5 or because of name property 5 if to each element of any row or column is added to k times corresponding elements of another row or column another row or column then the value of the determinant remains same so the other row or column or protective element k times or corresponding elements of another row or column or a 8 koro then the value of determinant remains same for each one I will determine a1, b1, c1 a2, b2, c2 a3, b3, c3 I will multiply the second row and add the first row to it then the value of determinant is k a1, k, a2 b1, k, b2 c1, k, c1 c2 a2, b2, c3 3, b3, c3 so a property to come any column or column r1, r1 plus k, r2 a2, r1 or what I mean k times of the elements of r2 I mean 8 koro so I mean a property any column a2, property 5 I mean to have a property or because of name property 6 if each element of any row or column is expressed as a sum of 2 elements then the determinant can be expressed as sum of 2 determinants of same order at a determinant term zhikunu roba column or protective elements nirogadu kodiyami 2nd elementor we sum sope pukhagbhe then hii determinantor we 2nd determinantor sum sope expresspora ami udharnagdara a property to ami alasana korou nirahal determinantood yasami a1, b1, b2 c1, b3 2, b 2, c 2, a 3, b 3, c 3. So, here a bottom row 2, ame dutta elemenisave pakak poriso, so a determinant of ame dutta determinisave express crossover. So, bottom determinant abo a 1, b 1, c 1, a 2, b 2, c 2, a 3, b 3, c 3. The second determinant abo d 1, d 2, d 3, a 2, b 2, c 3, a 3, b 3, c 3. So, ame paluze dutta determinisave signal row aba columnar, dutta elemento jodhi dutta elemenisave express hoyase. So, here a determinant abo ame dutta determinant of pakak poro. So, a 2 abo popart is 6. So, iman pori ame popart is of determinisave bika alasunaporlu. So, ame sota popart is of determinisave bika alasunaporlu. So, ame achi determinant unitor bika aji alasunaporlu. So, a unitor ame paluze determinant e hai, determinant bika ame alasunaporlu. Determinator order 2 or order 3 bika aji danilo. Hekot ame determinator sota popart is bika aji danilo palu. So, aji loi e class 2 imanute hamurenu mariso. So, next class on ame matrix or ame bika alasunaporlu matrix or adjoin of a matrix and inverse of a matrix or bika alasunaporlu. Namaskar.