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How do you find a basis of a vector space?
To find a basis of a vector space, you first need to identify a set of vectors that span the space. This typically involves collecting a set of linearly independent vectors from the space. You can use methods like the row reduction of a matrix, the Gram-Schmidt process, or simply examining the vectors directly to ensure they are independent. Finally, ensure that the number of vectors in your basis matches the dimension of the vector space.
Is it possible there is a vector space consisting of exactly two distinct vectors?
No, a vector space cannot consist of exactly two distinct vectors. A vector space must include the zero vector and be closed under vector addition and scalar multiplication. If there are only two distinct vectors, one must be the zero vector, and the other must be a scalar multiple of it, which contradicts the requirement for distinct vectors. Thus, a vector space must contain infinitely many vectors.
What is independent linearity?
Independent linearity refers to a property in linear algebra related to the linear independence of vectors in a vector space. A set of vectors is said to be linearly independent if no vector in the set can be expressed as a linear combination of the others. In terms of independent linearity, it implies that the vectors maintain their distinct contributions to the span of the space they occupy, ensuring that the maximum number of linearly independent vectors corresponds to the dimension of the space. This concept is crucial for understanding the structure and dimensionality of vector spaces.
What is the slope of 24 and 719?
24 and 719 is not enough information to define a slope. For 2-dimensional space two ordered pairs are the minimum required.
Is it true that combined vectors that go only forward or backward are one dimensional?
Yes, it is true. In a one-dimensional space, vectors can only extend in one direction, either forward or backward along a single axis. Any combination of such vectors will still lie along that same line, maintaining the one-dimensional nature of the space.
What must be the minimum number of vectors in a space is required so that their sum is zero?
If none of the individual vectors has a magnitude of zero, thenthe minimum number that can combined to make zero is two.
What are some sources of error in determining a resultant by adding vectors graphically?
Some sources of error in determining a resultant by adding vectors graphically include inaccuracies in measuring the lengths and angles of the vectors, mistakes in the scale or orientation of the vector diagram, and human error in drawing and aligning the vectors correctly on the graph. Additionally, errors can arise from distortion in the representation of vectors on a two-dimensional space when dealing with vectors in three dimensions.
What is meant by the resultant in physics?
In physics, the resultant is the vector sum of two or more vectors. It represents the net effect of all the individual vectors acting together. The resultant takes into account both the magnitude and direction of each vector to determine the overall effect.
Cross product is not difine in two space why?
When performing the cross product of two vectors (vector A and vector B), one of the properites of the resultant vector C is that it is perpendicular to both vectors A & B. In two dimensional space, this is not possible, because the resultant vector will be perpendicular to the plane that A & B reside in. Using the (i,j,k) unit vector notation, you could add a 0*k to each vector when doing the cross product, and the resultant vector will have zeros for the i & jcomponents, and only have k components.Two vectors define a plane, and their cross product is always a vector along the normal to that plane, so the three vectors cannot lie in a 2D space which is a plane.
When do you get a magnitude of 0 in vector?
The magnitude of a vector is 0 if the magnitude is given to be 0.The magnitude of the resultant of several vectors in n-dimensional space is 0 if and only if the components of the vectors sum to 0 in each of a sewt of n orthogonal directions.
How high is the required clear space on a basketball court?
The minimum required clear space on a basketball court depends on which kind of court it is. An NCAA court has a minimum of 25', while a recreational facility's minimum is 20'.
What is the minimum space required for a toilet and sink to be installed in a bathroom?
The minimum space required for a toilet and sink to be installed in a bathroom is typically around 30 inches by 60 inches.
What is the number of non co-planner unequal vectors required to produce zero resultant?
The answer given below (by myself) is wrong. The correct answer is four or more.It is possible to represent any set of vectors with a zero resultant as a closed straight-lined figure in 3-dimensional space (or in hyperspace with more dimensions).Any three points must make a triangle which is a plane shape, so the minimum number required for the vectors to be non coplanar is four. There is no maximum.All you need is a polygon, grab a couple of vertices and twist so that the shape is no longer planar.- - - - - - - - - -Three.ConsiderA = -i + 2jB = -2j + 3kandC = i -3kThenA is in the xy-planeB is in the yz-planeand C is in the xz-planeso they are non co-planar.Also|A| = sqrt(5)|B| = sqrt(13), and|C| = sqrt(10)so that A ≠B ≠C ≠ABut A + B + C = 0
When was Vectors in three-dimensional space created?
Vectors in three-dimensional space was created in 1978.
What is rational dimension?
Rational dimension refers to the dimension of a vector space over the field of rational numbers. It is the minimum number of linearly independent vectors needed to span the entire vector space. The rational dimension can differ from the ordinary dimension of a vector space if the vectors are over a field other than the rational numbers.
What is the minimum amount of space required for hamsters to live comfortably and thrive?
Hamsters need a minimum of 360 square inches of floor space in their enclosure to live comfortably and thrive.
When two vectors are acting at a point along different directions how do we determine magnitude and direction of the resultant?
The usual way to do this is to express each vector as the sum of two or three perpendicular vectors (two in a plane, three in 3D space). Then you can add the components of the two vectors, to get the new vector.For the case of two dimensions, on most scientific calculators there is a neat feature called rectangular-to-polar and polar-to-rectangular conversion, which can quickly convert a vector from polar (i.e., magnitude and angle) to rectangular (i.e., x-coordinate and y-coordinate), or vice versa.
