### Video Transcript

If the determinant of the matrix
one, π₯, π₯, three is equal to the determinant of the matrix two, one, four, three,
then π₯ equals blank.

We recall that the determinant of
any two-by-two matrix of the form π, π, π, π is equal to ππ minus ππ. Letβs begin by looking at the
matrix one, π₯, π₯, three. Multiplying the top-left and
bottom-right values gives us three. Multiplying the top-right and
bottom-left values gives us π₯ squared. This means the determinant of this
matrix is three minus π₯ squared. We can repeat this process for our
second matrix. Two multiplied by three is equal to
six. One multiplied by four is equal to
four. As six minus four is equal to two,
the determinant of this matrix is two.

In order to calculate the value of
π₯, we need to solve the equation three minus π₯ squared is equal to two. We can add π₯ squared and subtract
two from both sides of this equation. This gives us three minus two is
equal to π₯ squared. As π₯ squared is equal to one, we
can square root both sides of this equation. The square root of one is equal to
one. This means that π₯ could be
positive one or negative one, as after square rooting a number, our answer can be
positive or negative. If the determinant of the two
matrices are equal, then π₯ can be equal to one or negative one.

We could check this answer by
substituting these values back into the expression three minus π₯ squared. Squaring one or negative one gives
us an answer of one. Therefore, we have three minus
one. As this is equal to two, which was
the determinant of the second matrix, we know that our answers are correct. π₯ can be equal to one or negative
one.