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Linear Algebra Essentials: Vectors, Matrices & Solutions Flashcards

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Algebra - Linear Algebra

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user_hodr Created by 9 mon ago

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Cards in this deck(35)
is a location in space.
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a quantity that has both magnitude and direction they are denoted as a variable(a, x, v) with an arrow on top.
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a rectangular array of numbers.
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row by column(mxn)
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is a free variable or something that needs to be parametrized.(unpivoted column)
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the variable that has a pivotal 1.
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objects that split space into 2 pieces( 2
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is to swap the rows for column and columns for rows.
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are constant that are denoted as ||v||.
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a system of equations
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1. the first nonzero number in every entry in each row is a 1(pivotal/leading) 2. the leading one in any row is the right of the leading 1 above and below. 3. if there are a row of 0s that's at the bottom.
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all statements of REF hold true as well 1. all of the other entries with the leading 1 in their column need to be a 0.
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is when you do not have a free variable and all the rows/column have a leading 1.
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when there are free variables in the matrices.
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there is an untrue statement ( 9=0).
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True
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True(This is because there can only be a pivotal one in each row which in this problem tells us equations, which are our rows is less than the variables meaning some variables have to be free.
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False just for the fact that there could be an untrue statement.
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true
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variables
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a1v1, a2v2, ..., anvn which is a single vector. The mathematic definition is multiplying each vector by a constant and add them all together.
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no vectors in a set can be written as a linear combination of the other vectors. Another definition is that all the vectors are equal to 0 is the only answer. Also all the vectors are going into different directions. ALL OF THE VECTORS HAVE TO BE UNRELATED TO EACHOTHER!!!
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vectors are multiples of each other, also it can be said that we can have a constant/scalar that can get us to equal the other vector.
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Get the augumented matrix in RREF and then us should get this equation #u+#v,
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rows
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column
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m x 1
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m x n
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n x 1
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the set of all linear combinations of those vectors.
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left to right
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right to left
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a nonzero solution of a homogeneous equation or system of homogeneous equations or just an equation with a free variable
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False (These two space have nothing to do with each other)
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False its linear combination
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