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[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.
inverse matrix 2x2 formula

[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
2x2 matrix inverse calculator

[DOC File]Definitions
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Inverse of a Matrix: As long as the determinant is not zero, the inverse of a 2x2 matrix is . A = = For example, A = = = The inverse matrix is used in systems of equations to find variables x, y, and z: If the determinant is zero, either there are an infinite number of solutions or there are no solutions.
2x2 inverse calculator

[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.
modular inverses of 2x2 matrices

[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\
2x2 inverse calc

[DOC File]Vectors and Matrices
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Jan 20, 2009 · The simplest application of this equation is to a 2x2 matrix. For such a matrix, [54] Combining the results of equation [54] with equation [40] for a 2x2 determinant, gives the following result for the inverse of a 2x2 matrix. [55] You can easily show that this is correct by multiplying the original matrix by its inverse.
inverse of 3x3 matrix

[DOC File]Investigation: Solving Equations Using Inverse Matrices
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Since matrix multiplication is no commutative, the order in which we multiply the matrices is very important. The inverse will always go first, so the equation will look like this: AX= B. A-1AX = A-1B We need to multiply by the inverse to both sides. notice how the inverse …
2x2 matrix times 2x2

[DOCX File]Rotation Matrices
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Equations 1.0 and 1.1 illustrate the important idea that a matrix can be thought of as the “instructions” for a linear transformation of a vector to another vector. 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).
inverse of a 2x2 matrix

2x2 matrix with no inverse