ssrs barcode font free First we generate two 3 3 random matrices as lists. in Software

Create QR Code in Software First we generate two 3 3 random matrices as lists.

EXAMPLE 8 First we generate two 3 3 random matrices as lists.
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m1 = Table[RandomInteger[9], {i, 1, 3}, {j, 1, 3}]
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4, 2}, {2, 9, 3}, {0, 1, 4}} 8, 1}, {8, 3, 4}, {6, 4, 0}}
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m2 = Table[RandomInteger[9], {i, 1, 3}, {j, 1, 3}]
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Now we look at them in matrix form. m1 // MatrixForm 9 4 2 2 9 3 0 1 4 m2 // MatrixForm 2 8 1 8 3 4 6 4 0
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Linear Algebra
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The next operation multiplies each element of m1 by 5. 5 m1 45 20 10 10 45 14 0 5 20 Next compute their sum, difference, and product. m1 + m2 // MatrixForm 11 12 3 10 12 7 6 5 4 m1 - m2 // MatrixForm 7 4 1 6 6 1 6 3 4 m1. m2 // MatrixForm 62 92 25 94 55 38 32 19 4 Care must be taken not to use * between the matrices to be multiplied, as this simply multiplies corresponding entries of the matrices, in accordance with list conventions. m1 * m2 // MatrixForm 18 32 2 16 27 12 0 4 0
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EXAMPLE 9
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v1 = {1, 2, 3}; v2 = {4, 5, 6}; v1.v2 32 Cross[v1, v2] { 3, 6, 3}
Mathematica expresses the dot product as a number rather than as a list containing a single entry.
Mathematica makes no distinction between row and column vectors. Therefore, if v is an n-dimensional vector and m is an n n matrix, both v.m and m .v are defined (although they generally yield different results). Furthermore, if v1 is an n 1 matrix (row vector) and v2 is a 1 n matrix (column vector), v1.v2 should be an n n matrix, but Mathematica still computes a dot product. The command Outer can be used to compute the outer product of two vectors.
Outer[Times, v1, v2] computes the outer product of v1 and v2. (Outer is much more general and can be used for other purposes. See the Documentation Center for additional information.)
Linear Algebra
EXAMPLE 10
v1 = {1, 2, 3}; v2 = {4, 5, 6}; m = {{1, 2, 2}, {2, 3, 3}, {3, 1, 2}}; m //MatrixForm 1 2 2 2 3 3 3 1 2 m.v1
{11,
17, 11}
1 2 2 1 11 2 3 3 2 = 17 3 1 2 3 11 1 3) 2 3
2 3 1 2 14 3 = 11 14 2
v1.m
{14,
11, 14}
Outer[Times, v1, v2] // MatrixForm 4 5 6 8 10 12 12 15 18
1 4 5 6 2 ( 4 5 6 ) = 8 10 12 3 12 15 18
Inverse[matrix] computes the inverse of matrix. Det[matrix] computes the determinant of matrix. Transpose[matrix] computes the transpose of matrix. Tr[matrix] computes the trace of matrix. MatrixPower[matrix, n] computes the nth power of matrix. Minors[matrix] produces a matrix whose (i, j)th entry is the determinant of the submatrix obtained from matrix by deleting row n i +1 and column n j +1. (matrix must be square.) Minors[matrix, k] produces the matrix whose entries are the determinants of all possible k k submatrices of matrix. (matrix need not be square.)
EXAMPLE 11
1 2 2 m1 = 2 3 3 ; 3 4 5 1 2 3 4 m2 = 5 6 7 8 ; 9 10 11 12 Inverse[m1] //MatrixForm 3 2 0 1 1 1 1 2 1 Tr[m1] 9 MatrixPower[m1, 3] // MatrixForm 97 142 160 151 221 249 231 338 381
These, and subsequent examples, were created using Create Table/Matrix in the Insert menu.
Linear Algebra
Transpose[m2] //MatrixForm 1 2 3 4 5 9 6 10 7 11 8 12
The matrix does not have to be square in order for its trace to be de ned.
Tr[m2]
EXAMPLE 12
m = Table[a[i, j], {i, 1, 3}, {j, 1, 3}]; m //MatrixForm a[1,1] a[1,2] a[1,3] a[2,1] a[2,2] a[2,3] a[3,1] a[3,2] a[3,3] [ Minors[m] //MatrixForm
, a[1,2]a[2,1]+ a[1,1]a[2,2] a[1,3]a[2,1]+ a[1,1]a[2,3] a[1,3]a[2,2]+ a[1,2]a[2,3] a[1,2]a[3,1]+ a[1,1]a[3, a 2] a[1,3]a[3,1]+ a[1,1]a[3,3] a[1,3]a[3,2]+ a[1,2]a[3,3] , + 2 a[2,2]a[3,1]+ a[2,1]a[3,2] a[2,3]a[3,1]+ a[2,1]a[3,3] a[2,3]a[3,2]+ a[2,2]a[3,3]
SOLVED PROBLEMS
12.8 The (Euclidean) norm of a vector is the square root of the sum of the squares of its components. Compute the norm of the vector (1, 3, 5, 7, 9, 11, 13, 15).
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