Element **A matrix can be named using its dimensions Determinant for a 3x3 matrix: Expansion by minors Example: Solve using the inverse matrix method
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[PDF] Matrix Inverses and Determinants - Kuta Software
Worksheet by Kuta Software LLC -2- Find the inverse of each matrix 11) -3 1 9 -1 12) -3 -3 -4 -3 13) -4 0 -8 -1 14) 3 -1 -2 4 For each matrix state if an
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3x3 matrix inverse A = ⎛⎝ 1 −1 1 0 −2 1 −2 −3 0 ⎞ ⎠ (AI) = ⎛⎝ 1 − 1 1 1 0 0 0 −2 1 0 1 0 −2 −3 0 0 0 1 ⎞ ⎠ ⎛1 −1 1 1 0 0⎞ ⎛1 −1 1 1
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Step 3: find the matrix of cofactors by changing the sign of the four elements just around the center element to its opposites 11 8 7 5 4 3 3 2 1 -
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Worksheet by Kuta Software LLC Extra Practice - Determinants Inverses of Matrices Evaluate each determinant 1) -5 -3 3 3 -3 -4 4 1 -5 0 -1 -4 7) -3 4 -5 2 -3 -5 1 3 5 8) 0 5 -4 -3 4 -5 1 0 -5 9) Find the inverse of each matrix
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Worksheet by Kuta Software LLC For each matrix state if an inverse exists 1) - 3 -4 6 3 2) -2 -2 Find, by hand, the inverse of each matrix 5) 9 9 0 -8 6)
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Calculate the determinant of 2x2 and 3x3 matrices • Use the determinant Distribute worksheets “Matrix Inverse Roundtable 1–4” to each group Circulate the
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In this leaflet we consider how to find the inverse of a 3×3 matrix Before you work through this leaflet, you will need to know how to find the determinant and
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Element **A matrix can be named using its dimensions Determinant for a 3x3 matrix: Expansion by minors Example: Solve using the inverse matrix method
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If we know matrix and matrix , solve for the unknown matrix Find the inverse of a 2x2 matrix: Find the inverse 1 2 Worksheet by Kuta Software LLC Algebra 2
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Notes on Matrices 4-1-2 Definition of a Matrix Element **A matrix can be named using its dimensions. Dimension Examples: 1. A =2!1
05 !482. B =1
2 3 43. C =053!1
!2096Row Matrix Column Matrix Square Matrix Using matrices to solve problems: Jim, Mario and Mike are married to Shana, Kelly and Lisa. Mario is Kelly's brother and lives in Florida with his wife. Mike is shorter than Lisa's husband. Mike works at a bank. Shana and her husband live in Kentucky. Kelly and her husband work in a candy store. Who is married to whom? Find out using a matrix!
Matrices 2 Equal Matrices Solve for x and y. 1. 2x 2x+3y y 122. 3x+y
x!2y x+3 y!23. 2x33z
=53y9Adding and Subtracting Matrices Only matrices with ______________________________ can be added or subtracted. The resulting matrix has ___________________ dimensions. Examples 1. !204
3!1012
3!2!2 !460 !152!4 6712. 3!4
02 468024
3. 2!18
20!5 !42 !514. !3102
!108!6 010 543210
!8!10!4 Matrices 3 Scalar Multiplication Examples: 1. !27!10 2. 4 !20 4!5 3. !5 12!3 4!56 !78!9
Matrix Multiplication **Multiply rows times columns** **You can only multiply if the number of columns in the 1st matrix is equal to the number of rows in the 2nd matrix. 1. 21392
345762. 39221
576343. 1211
13272618
x y z
4. 0143
1025Matrices 4 Determinants Determinant of a 2x2 matrix: Find the determinant of each: 1. !5!7 118
2. 32 !15
3. 10!2
0!3**To find a determinant you must have a _________ matrix!! Determinant for a 3x3 matrix: Expansion by minors *minor of an element is the determinant formed when the row and the column containing that element are deleted! Examples: 1. !238
67!1!459
2. 5!12
2!35 32!33. !104
2!22 30!1Matrices 5 Determinant for a 3x3 matrix: Diagonal Method Examples: 1. !238 67!1
!459
2. 5!12
2!35 32!33. !104
2!22 30!1Solving Systems using Cramer's Rule Cramer's Rule:
Matrices 6 Identity and Inverse Matrices Identity Matrix Inverse of a 2x2 matrix Examples: 1. 53
212. 12 34
3. 2!5
07 ???Is there ever a square matrix that does not have an inverse???Matrices 7 Solving Systems of equations using matrices • Coefficient Matrix • Variable Matrix • Constant Matrix Example: 3!2
41x y 7 8 Steps to solving: 1. 2. 3. Example: Solve using the inverse matrix method 4x!12y=7 x+6y=9quotesdbs_dbs20.pdfusesText_26