# Video: Evaluating Determinants

Find the value of |π + π₯, 5π and π + 7π¦, β7π|.

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### Video Transcript

Find the value of the determinant of the matrix π plus π₯, five π, π plus seven π¦, negative seven π.

Remember, for a two-by-two matrix π΄ with elements π, π, π, π, its determinant can be found by subtracting the product of elements π and π from the product of elements π and π. In our matrix, the element π is given as π plus π₯. π is given as five π. π is π plus seven π¦. And π is negative seven π.

To find its determinant then, we need to find the product of π and π. Thatβs π plus π₯ multiplied by negative seven π. I inverted that as negative seven π multiplied by π plus π₯. Weβre then going to subtract the product of the elements in the top right and bottom left. Thatβs π and π. And weβre going to subtract five π multiplied by π plus seven π¦.

Weβll need to expand each of these brackets as normal. Negative seven π multiplied by π is negative seven ππ. And negative seven π multiplied by π₯ is negative seven ππ₯. Negative five π multiplied by π is negative five ππ. And negative five π multiplied by seven π¦ is negative 35ππ¦.

Finally, we need to simplify this expression by collecting like terms. Here, we have two terms that are some multiple of ππ. Negative seven ππ minus five ππ is negative 12ππ.

And therefore, the determinant of our matrix is negative seven ππ₯ minus 35ππ¦ minus 12ππ.