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Given that the matrix π΄ equals negative two, six, negative six, one, eight, four, find π΄ transpose.
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Just a quick reminder about this notation, first of all, when we see a matrix and then a superscript capital π, this means weβre being asked to find the transpose of the matrix π΄.
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Thatβs the matrix we get when we swap the rows and columns of the matrix π΄ around.
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Looking carefully at our matrix π΄, then, we can see that it has two rows and three columns.
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The matrix π΄ transpose, then, will have three rows and two columns.
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The number of rows in matrix π΄ is the number of columns in its transpose.
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And the number of columns in matrix π΄ is the number of rows in its transpose.
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The first row in matrix π΄ β so thatβs negative two, six, negative six β becomes the first column in its transpose matrix.
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So, we can fill in this first column.
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The second row of matrix π΄ β so thatβs one, eight, four β will become the second column in our matrix π΄ transpose.
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So, by swapping the rows and columns of matrix π΄ around, weβve found its transpose matrix.
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π΄ transpose is equal to the matrix negative two, one, six, eight, negative six, four.
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We can also look at individual elements of these two matrices.
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For example, the element that was in the first row and second column of matrix π΄ β so thatβs six β is now in the second row and first column of the transpose matrix.
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Their positioning of rows and columns has been swapped around.
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Once again, our matrix π΄ transpose is the three-by-two matrix negative two, one, six, eight, negative six, four.