Inverse of a 2x2 matrix
[DOCX File]Rotation Matrices
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A 2x2 matrix represents a transformation that maps the set of all 2D vectors, i.e. all points in the x-y plane, into a new set of 2D vectors (or, equivalently, a new set of points). A 3x3 matrix maps 3D vectors into 3D vectors. The transformation represented by matrix . R. v
[DOC File]Matrices
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If we calculate the inverse of matrix A the result is . whererefers to the determinant of matrix A, which is defined for a 2x2 matrix as . The fact that the determinant of A equals zero renders the product meaningless, because all elements of C will equal infinity, no matter what the values of the elements of matrix B might be.
[DOCX File]Matrices 2
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Now we discuss the topic of “matrix division” and apply this idea to solve a system of linear equations. We will define the inverse* of a matrix, for example B-1=inverse of B. Then, instead of dividing one matrix by another (C=A/B), w we will multiply by the inverse (C=B-1A). *It is really the multiplicative inverse of a matrix.
[DOC File]MATRICES
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Co-factor Cij = determinant of 2X2 matrix obtained by deleting row i and column j of A, prefixed by + or – according to following pattern… e.g. C23 is co-factor associated with a23, in row 2 and column 3. so delete row 2 and column 3 to give a 2X2 matrix. co-factor C23 is – determinant of 2X2 matrix (negative sign in position a23)
[DOC File]ALGEBRA 2 X
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(2x2 by hand and calculator, 3x3 by calculator only) 4.4 p.274 #1-11 (use Calc for 10 and 11), 29, 38, 39 8 Review Matrix Multiplication Finding Matrix Inverses, Solving Systems Using Matrix Inverses 4.5 p.282-285 #1-12 9 Row Operations and Augmented Matrices for Solving Systems\
GRADE K
The determinant of a square matrix is nonzero if and only if the matrix has a multiplicative inverse. ( HS.MP.2. Reason abstractly and quantitatively. HS.MP.6. Attend to precision. HS.N-VM.11. Multiply a vector (regarded as a matrix with one column) by a matrix of suitable dimensions to …
[DOC File]Investigation: Solving Equations Using Inverse Matrices
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1 The symbol x-1 indicates the multiplicative inverse of a number or object. Example: 3-1 = . This means that the multiplicative inverse of 3 is because , so they cancel each other out. Since we are trying to undo the matrix, , we are not dividing, but instead, we are going to multiply by its inverse. On your calculator, find the inverse. Step 2
[DOC File]Solving a System of Equations Using Matrices
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Determine the inverse of the coefficient matrix. Multiply both sides of the matrix equation by the inverse matrix. In order to multiply the matrices on the right side of the equation, the inverse matrix must appear in front of the answer matrix.(the number of columns in the first matrix must equal the number of rows in the second matrix).
[DOC File]Vectors and Matrices
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Jan 20, 2009 · It is not always possible to find the inverse. A square matrix that has no inverse is called a singular matrix. It is usually not necessary to find the inverse of a matrix. If necessary, you can find a numerical value of the inverse by the same process used to …
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