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The product cA of a number c (also called a scalar in this context) and a matrix A is computed by multiplying every entry of A by c: (), =, This operation is called scalar multiplication, but its result is not named "scalar product" to avoid confusion, since "scalar product" is often used as a synonym for "inner product". For example:
In Northern Ireland, a new grade C* was introduced in 2019 to line up with the English grade 5. In both systems, work below the grade G or 1 standard is denoted as 'Unclassified' (U). For comparison purposes, a grade C is considered equivalent to a 4, and an A is equivalent to a 7, and an 8 is equivalent roughly to an A*.
In other words, we can only multiply matrices and when the number of rows of matches the number of columns of . One can keep track of this fact by declaring an n × m {\displaystyle n\times m} matrix to be of type m → n {\displaystyle m\to n} , and similarly a p × q {\displaystyle p\times q} matrix to be of type q → p {\displaystyle q\to p} .
The parallelogram defined by the rows of the above matrix is the one with vertices at (0, 0), (a, b), (a + c, b + d), and (c, d), as shown in the accompanying diagram. The absolute value of ad − bc is the area of the parallelogram, and thus represents the scale factor by which areas are transformed by A.
Only a small proportion of candidates score an 'A' in any subject (from as little as 2% to a maximum of about 10% in subjects taken by highly select groups). A further 8–15% are likely to gain a 'B' and about 20–25% achieve a 'C' grade. The National Senior Certificate is a group certificate and records an aggregate mark.
Grading in education is the application of standardized measurements to evaluate different levels of student achievement in a course. Grades can be expressed as letters (usually A to F), as a range (for example, 1 to 6), percentages, or as numbers out of a possible total (often out of 100).
From 2012 figures, 79% with A*, 48% of A, 15% of B and 1% of grade C chose Maths in the 6th form. For English, History and Geography, 30% with grade B, and 10% with grade C chose the course in the 6th form. The House of Lords July 2012 report Higher Education in STEM Subjects recommended that everyone study some type of Maths after 16. For less ...
The Hilbert matrix is also totally positive (meaning that the determinant of every submatrix is positive). The Hilbert matrix is an example of a Hankel matrix. It is also a specific example of a Cauchy matrix. The determinant can be expressed in closed form, as a special case of the Cauchy determinant. The determinant of the n × n Hilbert ...