78 results for "combinations".
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Question in LSE MA100 (Bugs fixed, September 2018)
This is the question for week 9 of the MA100 course at the LSE. It looks at material from chapters 17 and 18.
Description of variables for part b:
For part b we want to have four functions such that the derivative of one of them, evaluated at 0, gives 0; but for the rest we do not get 0. We also want two of the ones that do not give 0, to be such that the derivative of their sum, evaluated at 0, gives 0; but when we do this for any other sum of two of our functions, we do not get 0. Ultimately this part of the question will show that even if two functions are not in a vector space (the space of functions with derivate equal to 0 when evaluated at 0), then their sum could nonetheless be in that vector space. We want variables which statisfy:
a,b,c,d,f,g,h,j,k,l,m,n are variables satisfying
Function 1: x^2 + ax + b sin(cx)
Function 2: x^2 + dx + f sin(gx)
Function 3: x^2 + hx + j sin(kx)
Function 4: x^2 + lx + m sin(nx)
u,v,w,r are variables satifying
u=a+bc
v=d+fg
w=h+jk
r=l+mn
The derivatives of each function, evaluated at zero, are:
Function 1: u
Function 2: v
Function 3: w
Function 4: r
So we will define
u as random(-5..5 except(0))
v as -u
w as 0
r as random(-5..5 except(0) except(u) except(-u))
Then the derivative of function 3, evaluated at 0, gives 0. The other functions give non-zero.
Also, the derivative of function 1 + function 2 gives 0. The other combinations of two functions give nonzero.We now take b,c,f,g,j,k,m,n to be defined as \random(-3..3 except(0)).
We then define a,d,h,l to satisfy
u=a+bc
v=d+fg
w=h+jk
r=l+mnDescription for variables of part e:
Please look at the description of each variable for part e in the variables section, first.
As described, the vectors V3_1 , V3_2 , V3_3 are linearly independent. We will simply write v1 , v2 , v3 here.
In part e we ask the student to determine which of the following sets span, are linearly independent, are both, are neither:both: v1,v2,v3
span: v1,v1+v2,v1+v2+v3, v1+v2+v3,2*v1+v2+v3
lin ind: v1+v2+v3
neither: v2+v3 , 2*v2 + 2*v3
neither:v1+v3,v1-2*v3,2*v1-v3
neither: v1+v2,v1-v2,v1-2*v2,2*v1-v2 -
Question in MATH 6005 2018_2019
Linear combinations of $2 \times 2$ matrices. Three examples.
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Question in Joseph's workspace
Linear combinations of $2 \times 2$ matrices. Three examples.
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Question in Harry's workspace
Determine if various combinations of vectors are defined or not.
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Question in Marie's Logic workspace
Linear combinations of $2 \times 2$ matrices. Three examples.
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Question in MATH6005 Engineering Mathematics 101
Linear combinations of $2 \times 2$ matrices. Three examples.
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Question in MATH6005 Engineering Mathematics 101
Linear combinations of $2 \times 2$ matrices. Three examples.
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Question in Katherine's workspace
No description given
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Question in AMRC Maths Bridging Course
No description given
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Question in FY001 - Core Mathematics
No description given
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Question in FY001 - Core Mathematics
No description given
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Question in pre-algebra Numeracy and Arithmetic
No description given
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Question in Algebra
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Exam (3 questions) in mathcentre
Three questions on linear combinations and products of matrices.
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Exam (5 questions) in mathcentre
5 questions on vectors. Scalar product, angle between vectors, cross product, when are vectors perpendicular, combinations of vectors defined or not.
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Exam (5 questions) in Maths Support Wiki
5 questions on vectors. Scalar product, angle between vectors, cross product, when are vectors perpendicular, combinations of vectors defined or not.
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Question in Katie's workspace
Linear combinations of $2 \times 2$ matrices. Three examples.
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Question in Bill's workspace
Linear combinations of $2 \times 2$ matrices. Three examples.