Download Mental Maths Book 1 (Bk.1) by Anne Foster PDF
By Anne Foster
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B5. B6. B7. Applied Linear Algebra Elementary Linear Algebra Elementary Linear Algebra with Applications Linear Algebra and Its Applications Linear Algebra with Applications Matrix Algebra with Applications Matrix Theory The collection of keywords is given by the following alphabetical list: algebra, application, elementary, linear, matrix, theory For a simple matching search, we just use 0’s and 1’s, rather than relative frequencies, for the entries of the database matrix. Thus, the (i, j) entry of the matrix will be 1 if the ith word appears in the title of the jth book and 0 if it does not.
03 To search for these two words, we take our search vector x to be the vector whose entries x6 and x8 are both equal to 1 and whose remaining entries are all 0. 08 Note that 16 of the 200 words (8 percent of the words) in document 9 match the key search words. If yj is the largest entry of y, this would indicate that the jth document in the database is the one that contains the keywords with the greatest relative frequencies. Advanced Search Methods A search for the keywords linear and algebra could easily turn up hundreds of documents, some of which may not even be about linear algebra.
The matrix equation (7) provides a nice way of characterizing whether a linear system of equations is consistent. Indeed, the following theorem is a direct consequence of (7). 1 Consistency Theorem for Linear Systems A linear system Ax = b is consistent if and only if b can be written as a linear combination of the column vectors of A. EXAMPLE 7 The linear system x1 + 2x2 = 1 2x1 + 4x2 = 1 ⎧ ⎫ ⎭ cannot be written as a linear combination of the ⎩1⎪ is inconsistent since the vector ⎪ 1 ⎧ ⎫ ⎧ ⎫ ⎭.