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( 6 4 - 23) zero matrix - all elements are o identity matrix diagonot left are all ones. adding / subtracting. (63) (39) · (42) 03 (²6) 2x2 matrix. square matrix -34 3 ( 2 - ³ 4 ) - ( § 2 2 ) - ( 13 - 5³₂) = 1 23 -2 multiplying → multiply every element by scalar A = (-1²) find 2A: • (224) 5-1 2 83-4 + → matrix multiplication no of rows in 2nd AB - only if A is nxm and B is mx k ABBA x 5x2+1x9 22 9-3 74 det m=0 det m / 0 15 21 15 -9 + 2x7 = 15 Determinants. 2x2 matrix bm= (ab) no columns in 1st det m= ad-bc singular non-singular 2x4 matrix (₂³) (₁-²²) (-1) 100 O 0 ( 34 ) × (-²) ↓ = 13 you CANNOT add matrices of different sizes Ix-3+-2x2---7 3x-3+4x2 if A and Bare non-singular then (AB) =A"B₁¹ mm ¹ = m²m = 1 P and Q are non-singular matrices. Prove that (PQ) = Q-P-¹ C (PQ) then (PQIC = I. PPQC = PI (PP)QC = PI So QC = P QỐC=G P IC = Q P cancelled out I C=QP So (PQ) Q P as required. 3x3 matrix Inversing 42x2 matrix m a b c des) = a (ef) - b (gf) + (( de ) 9 hi gh = 3x3 matrix m-¹: det m : Use the definition of inverse A-¹A=I=AA-¹ 1 det m Multiply on the left by P Remember P-P=1, IQ-Q and PI = P¹, ст Multiply on the left by Q Use Q¹Q=L d-b (a+b) -ca change sign Switch places if A (2) - v then (4) = A¯`v =V find matrix of minors After one year: • the number of adult males...
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Alternative transcript:
had increased by 2% • the number of adult females had increased by 3% • the number of youngsters had decreased by 4% • the total number of mole-rats had decreased by 20 Form and solve a matrix equation to find out how many of each type of mole-rat were in the original colony. m= cofactor 191|gk| Teac Example 21 A colony of 1000 mole-rats is made up of adult males, adult females and youngsters. Originally there were 100 more adult females than adult males. transpose (CT) j mp -к и -а tor CT= jkl mno pqr Problem-solving Assign a letter to each unk then work your way throug text using the information equations. C= abc del ghl work through like this abe abe def ghi def ghi Solving systems you can use the INVERSE of a 3x3 matrix to solve simultaneous equations with 3 unknowns J - K L -m n.o p-qr change sign of these 4 rows turn into the column M+F+y=1000 F-M - 100 M-F=-100 1.02 m +1.03 F +0.96 Y = 980 Convert into a matrix A (10₂ I 1 1.02 103 = I -96 13 ) (*) . (100) 980 (4) O 0.96 7 100⁰ 96 -6 100 205 -1 -200 1-96 7 10 01 96 -6 100 (205 -1 -200 8) (1100) 980 A-₁ ( 10001 -100 980 (4) /1001 200 700 100 adult males, 200 adult female and 700 youngsters.
Chapter 6 of further core one. Multiplying, determinants, and inversing.
Ahmed Nour ✓™
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Chapter 6 of further core one. Multiplying, determinants, and inversing.
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( 6 4 - 23) zero matrix - all elements are o identity matrix diagonot left are all ones. adding / subtracting. (63) (39) · (42) 03 (²6) 2x2 matrix. square matrix -34 3 ( 2 - ³ 4 ) - ( § 2 2 ) - ( 13 - 5³₂) = 1 23 -2 multiplying → multiply every element by scalar A = (-1²) find 2A: • (224) 5-1 2 83-4 + → matrix multiplication no of rows in 2nd AB - only if A is nxm and B is mx k ABBA x 5x2+1x9 22 9-3 74 det m=0 det m / 0 15 21 15 -9 + 2x7 = 15 Determinants. 2x2 matrix bm= (ab) no columns in 1st det m= ad-bc singular non-singular 2x4 matrix (₂³) (₁-²²) (-1) 100 O 0 ( 34 ) × (-²) ↓ = 13 you CANNOT add matrices of different sizes Ix-3+-2x2---7 3x-3+4x2 if A and Bare non-singular then (AB) =A"B₁¹ mm ¹ = m²m = 1 P and Q are non-singular matrices. Prove that (PQ) = Q-P-¹ C (PQ) then (PQIC = I. PPQC = PI (PP)QC = PI So QC = P QỐC=G P IC = Q P cancelled out I C=QP So (PQ) Q P as required. 3x3 matrix Inversing 42x2 matrix m a b c des) = a (ef) - b (gf) + (( de ) 9 hi gh = 3x3 matrix m-¹: det m : Use the definition of inverse A-¹A=I=AA-¹ 1 det m Multiply on the left by P Remember P-P=1, IQ-Q and PI = P¹, ст Multiply on the left by Q Use Q¹Q=L d-b (a+b) -ca change sign Switch places if A (2) - v then (4) = A¯`v =V find matrix of minors After one year: • the number of adult males...
( 6 4 - 23) zero matrix - all elements are o identity matrix diagonot left are all ones. adding / subtracting. (63) (39) · (42) 03 (²6) 2x2 matrix. square matrix -34 3 ( 2 - ³ 4 ) - ( § 2 2 ) - ( 13 - 5³₂) = 1 23 -2 multiplying → multiply every element by scalar A = (-1²) find 2A: • (224) 5-1 2 83-4 + → matrix multiplication no of rows in 2nd AB - only if A is nxm and B is mx k ABBA x 5x2+1x9 22 9-3 74 det m=0 det m / 0 15 21 15 -9 + 2x7 = 15 Determinants. 2x2 matrix bm= (ab) no columns in 1st det m= ad-bc singular non-singular 2x4 matrix (₂³) (₁-²²) (-1) 100 O 0 ( 34 ) × (-²) ↓ = 13 you CANNOT add matrices of different sizes Ix-3+-2x2---7 3x-3+4x2 if A and Bare non-singular then (AB) =A"B₁¹ mm ¹ = m²m = 1 P and Q are non-singular matrices. Prove that (PQ) = Q-P-¹ C (PQ) then (PQIC = I. PPQC = PI (PP)QC = PI So QC = P QỐC=G P IC = Q P cancelled out I C=QP So (PQ) Q P as required. 3x3 matrix Inversing 42x2 matrix m a b c des) = a (ef) - b (gf) + (( de ) 9 hi gh = 3x3 matrix m-¹: det m : Use the definition of inverse A-¹A=I=AA-¹ 1 det m Multiply on the left by P Remember P-P=1, IQ-Q and PI = P¹, ст Multiply on the left by Q Use Q¹Q=L d-b (a+b) -ca change sign Switch places if A (2) - v then (4) = A¯`v =V find matrix of minors After one year: • the number of adult males...
Can't find what you're looking for? Explore other subjects.
Knowunity is the # 1 ranked education app in five European countries
Knowunity was a featured story by Apple and has consistently topped the app store charts within the education category in Germany, Italy, Poland, Switzerland and United Kingdom. Join Knowunity today and help millions of students around the world.
Still not sure? Look at what your fellow peers are saying...
iOS User
I love this app so much [...] I recommend Knowunity to everyone!!! I went from a C to an A with it :D
Stefan S, iOS User
The application is very simple and well designed. So far I have found what I was looking for :D
SuSSan, iOS User
Love this App ❤️, I use it basically all the time whenever I'm studying
Alternative transcript:
had increased by 2% • the number of adult females had increased by 3% • the number of youngsters had decreased by 4% • the total number of mole-rats had decreased by 20 Form and solve a matrix equation to find out how many of each type of mole-rat were in the original colony. m= cofactor 191|gk| Teac Example 21 A colony of 1000 mole-rats is made up of adult males, adult females and youngsters. Originally there were 100 more adult females than adult males. transpose (CT) j mp -к и -а tor CT= jkl mno pqr Problem-solving Assign a letter to each unk then work your way throug text using the information equations. C= abc del ghl work through like this abe abe def ghi def ghi Solving systems you can use the INVERSE of a 3x3 matrix to solve simultaneous equations with 3 unknowns J - K L -m n.o p-qr change sign of these 4 rows turn into the column M+F+y=1000 F-M - 100 M-F=-100 1.02 m +1.03 F +0.96 Y = 980 Convert into a matrix A (10₂ I 1 1.02 103 = I -96 13 ) (*) . (100) 980 (4) O 0.96 7 100⁰ 96 -6 100 205 -1 -200 1-96 7 10 01 96 -6 100 (205 -1 -200 8) (1100) 980 A-₁ ( 10001 -100 980 (4) /1001 200 700 100 adult males, 200 adult female and 700 youngsters.