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Can a vector space have exactly two distinct vectors in it?
No.A vector space is a set over a field that has to satisfy certain rules, called axioms. The field in question can be Z2 (see discussion), but unlike a field, a vector's inverse is distinct from the vector. Therefore, in order to satisfy the "inverse elements of addition" axiom for vector spaces, a vector space must minimally (except if it is the null space) have three vectors, v, 0, and v-1. The null space only has one vector, 0.Field's can allow for two distinct elements, unlike vector spaces, because for any given element of a field, for example a, a + (-a) = 0 meets the inverse axiom, but a and -a aren't required to be distinct. They are simply scalar magnitudes, unlike vectors which can often be thought of as having a direction attached to them. That's why the vectors, v and -v are distinct, because they're pointing in opposite directions.
Can a vector be represented in terms of unit vector?
Yes, a vector can be represented in terms of a unit vector which is in the same direction as the vector. it will be the unit vector in the direction of the vector times the magnitude of the vector.
How will you get the resultant of all vectors?
Graphical Vector AdditionDraw your first vector. Then draw the tail (start) of your second vector at the tip (end) of your first vector. Then draw the tail of your third vector at the tip of you third vector (if it exists,) and so on. To find the resultant, draw a vector from the tail of the first vector to the tip of the last vector. The angle of the resultant will be between the resultant's tail and the first vector's tail. To find these values, it is recommended that you use a scale (e.g. 1cm:1m) and a protractor so that your values are accurate.Or, to do it mathematically (with 2 vectors):You have vector a with angle Ao, and vector b with angle Bo.To get vector c (resultant,) break the vectors up into their x and y components, then add the x and y components to find the x and y of the resultant. To find the magnitude of vector c, use Pythagoras's theorem, a2 + b2 = c2. To find the angle of c, use inverse tangent, tan-1(y/x)Example:Remember that sin = y and cos = x. Thus, to find the x component of a vector, use cos, and to find the y component of a vector, use sin.c = square root( (acosA + bcosB)2 + (asinA + bsinB)2 )angle of c = tan-1( (asinA + bsinB)/(bcosA + bcosB) )
Definition of Inverse property of addition?
* *It is the reverse of the actionEx.Addition is the inverse of subtrationmultiplication is the inverse of division
What are the two sets of inverse operations?
Addition is the inverse operation of subtraction and multiplication is the inverse operation of division. The word inverse means "opposite".
Why vector division is not possible?
In the case of the dot product, you would need to find a vector which, multiplied by another vector, gives a certain real number. This vector is not uniquely defined; several different vectors could be used to give the same result, even if the other vector is specified. For the other two common multiplications defined for vector, the inverse of multiplication, i.e. the division, can be clearly defined.
Can a vector space have exactly two distinct vectors in it?
No.A vector space is a set over a field that has to satisfy certain rules, called axioms. The field in question can be Z2 (see discussion), but unlike a field, a vector's inverse is distinct from the vector. Therefore, in order to satisfy the "inverse elements of addition" axiom for vector spaces, a vector space must minimally (except if it is the null space) have three vectors, v, 0, and v-1. The null space only has one vector, 0.Field's can allow for two distinct elements, unlike vector spaces, because for any given element of a field, for example a, a + (-a) = 0 meets the inverse axiom, but a and -a aren't required to be distinct. They are simply scalar magnitudes, unlike vectors which can often be thought of as having a direction attached to them. That's why the vectors, v and -v are distinct, because they're pointing in opposite directions.
What is the -matrix of groups-identity of matrix-inverse matrix-multiplication of matrices?
The eigen values of a matirx are the values L such that Ax = Lxwhere A is a matrix, x is a vector, and L is a constant.The vector x is known as the eigenvector.
Does vector subtraction commutes?
Vector addition is basically similar, with respect to many of its properties, to the addition of real numbers.A + B = B + ASubtraction is the inverse of addition: A - B = A + (-B), where (-B) is the opposite vector to (B).A - B is not usually the same as B - A. Therefore, it is not commutative.However, if you convert it to an addition, you can apply the commutative law: A + (-B) = (-B) + A.
What is acceleration a scalar or vector quantity?
A vector. Acceleration is defined as change in velocity in a given time, in symbolsa = ( v - u ) / t(the bolded symbols represent vectors)t is a scalar so its inverse is also a scalar.( v - u ) is a vector soa = vector * scalar = a vector.Answer2:Acceleration like many quantities is a Quaternion, consisting of a scalar part and a vector part. a= mv2/r is a scalar acceleration and A=dV/dt is a vector acceleration as is cV/r = A.
What are the two types of inverse functions?
These are the for inverse operations:Multiplications inverse is divisionDivisions inverse is multiplicationAdditions inverse is subtractionSubtractions inverse is addition
How do you inverse in french?
"Inverse"
Why do square matrices only have multiplicative inverses?
there are pseudo inverses for non-square matrices a square matrix has an inverse only if the original matrix has full rank which implies that no vector is annihilated by the matrix as a multiplicative operator
Name the additive inverse and the multiplicative inverse for the number 2.5?
Additive inverse: -2.5 Multiplicative inverse: 0.4
What is the inverse of subtraction?
Addition is the inverse of Subtraction. Division is the inverse of Multiplication. and then visa-versa. :-) Addition is the inverse of Subtraction. Division is the inverse of Multiplication. and then visa-versa. :-) the Answer is subtraction
Can a vector be represented in terms of unit vector?
Yes, a vector can be represented in terms of a unit vector which is in the same direction as the vector. it will be the unit vector in the direction of the vector times the magnitude of the vector.
How will you get the resultant of all vectors?
Graphical Vector AdditionDraw your first vector. Then draw the tail (start) of your second vector at the tip (end) of your first vector. Then draw the tail of your third vector at the tip of you third vector (if it exists,) and so on. To find the resultant, draw a vector from the tail of the first vector to the tip of the last vector. The angle of the resultant will be between the resultant's tail and the first vector's tail. To find these values, it is recommended that you use a scale (e.g. 1cm:1m) and a protractor so that your values are accurate.Or, to do it mathematically (with 2 vectors):You have vector a with angle Ao, and vector b with angle Bo.To get vector c (resultant,) break the vectors up into their x and y components, then add the x and y components to find the x and y of the resultant. To find the magnitude of vector c, use Pythagoras's theorem, a2 + b2 = c2. To find the angle of c, use inverse tangent, tan-1(y/x)Example:Remember that sin = y and cos = x. Thus, to find the x component of a vector, use cos, and to find the y component of a vector, use sin.c = square root( (acosA + bcosB)2 + (asinA + bsinB)2 )angle of c = tan-1( (asinA + bsinB)/(bcosA + bcosB) )
