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Determine which of the following matrices is a column matrix.
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Is it (A) two, negative two, three, five?
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(B) Two, negative two, three.
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Is it (C) two, zero, zero, five?
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Is it (D) zero, zero, zero, zero?
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Or is it (E) two, negative two, three?
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Letβs remind ourselves what we mean when we say that a matrix is a column matrix.
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We say that an π by π matrix or a matrix order π by π has π rows and π columns.
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Now, if π is equal to one, we call this a column matrix.
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In other words, if the matrix only has one column, itβs a column matrix.
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So letβs find the order of each of our individual matrices.
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Matrix π΄ has two rows and two columns, so itβs a two-by-two matrix.
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Matrix π΅ has three rows and one column, so itβs a three by one.
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Matrix πΆ is again a two by two, as is matrix π·.
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And then we have the matrix πΈ, which has one row and three columns.
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So thatβs one by three.
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Now, if we look carefully and we compare each of these to our definition, we see that the matrix which has a value of π equal to one is the matrix π΅.
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And so the matrix which is a column matrix is indeed π΅.
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Now, in fact, weβre also able to name the other types of matrices.
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When π is equal to π, in other words, when the number of rows is equal to the number of columns, we say the matrix is square.
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So matrix π΄ is square, as is matrix πΆ.
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Now, matrix π· is also square, but this is a special type of matrix in itself.
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Every single element in this matrix is zero.
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And when we have a square matrix where this is the case, we call this a null matrix or zero matrix.
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And then, finally, letβs consider the matrix πΈ.
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This time, the value of π is equal to one.
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There is simply one row, and so we call this a row matrix.