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Given that π΄ equals to negative seven, seven and π΅ equals to zero, negative five, find π΄π΅ if possible.
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You can multiply two matrices if and only if the number of columns in the first matrix equals the number of rows in the second.
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Otherwise, the product of two matrices is undefined.
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Here matrix π΄ has one column and matrix π΅ has one row.
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So we can multiply these matrices.
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To find π΄π΅ then, which is the product of matrix π΄ and matrix π΅, we need to do the dot product.
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Letβs do this for the first row in π΄ and the first column in π΅.
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Negative seven multiply by zero is zero.
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The first element in a matrix π΄π΅ is therefore zero.
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Then we multiply the elements in our first row of π΄ by the second element in π΅.
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Negative seven multiplied by negative five is 35.
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The element in the first row and second column of the product of π΄π΅ is therefore 35.
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Multiplying seven by zero gives us zero.
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The element in the first column and the second row of our product is therefore zero.
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Finally, we multiply seven by negative five to give us negative 35.
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And the final element of a product π΄π΅ is negative 35.
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In this case then, π΄π΅ is entirely possible and its matrix is as shown.