WEBVTT
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Find the determinant of the two-by-two matrix five, zero, zero, five.
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In this question, weβre given a two-by-two matrix, and weβre asked to find the determinant of this matrix.
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So, the first thing weβre going to need to do is recall what we mean by the determinant of a matrix.
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First, recall we can use this vertical bar notation to represent the determinant of a matrix.
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Next, we need to recall how we actually calculate the determinant of this matrix.
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To do this, we need to recall the determinant of a two-by-two matrix is the difference between the products of its diagonals.
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So, this gives us the determinant of the two-by-two matrix ππ minus ππ is equal to the product of the first diagonal, π times π, minus the product of the second diagonal, ππ.
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We can use this to find the determinant of the matrix given to us in the question.
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We need to calculate the determinant of the two-by-two matrix five, zero, zero, five.
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First, we need to calculate the product of five multiplied by five.
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Then, we need to subtract the product of zero multiplied by zero.
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So, the determinant of this matrix is five multiplied by five minus zero multiplied by zero.
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And we can calculate this.
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Itβs just equal to 25.
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And this gives us our final answer of 25.
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And itβs also worth pointing out we could have thought about this as a formula for finding the two-by-two determinant, where we substitute π is equal to five, π is equal to five, and π and π are both equal to zero.
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This would also give us the correct answer of 25.
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Therefore, we were able to show the determinant of the two-by-two matrix five, zero, zero, five is equal to 25.