i'm not sure how to go about this one. any help would be appreciated!

find all x's that would make the 2x2 matrix below = to a shear-dilation:

1st row: 1, x
2nd row: 3, 4

To find the values of x that would make the given 2x2 matrix equal to a shear-dilation matrix, we need to understand the properties of a shear-dilation matrix.

A shear-dilation matrix is a linear transformation that combines both shear and dilation. It can be represented by the following 2x2 matrix form:

1 k
h 1

Where k represents the dilation factor and h represents the shear factor. For a matrix to be a shear-dilation matrix, there should be a single value for both k and h.

Given the matrix:

1 x
3 4

To determine the values of x that would make it a shear-dilation matrix, we need to compare it with the general form of a shear-dilation matrix.

Comparing the first row of the given matrix with the general form, we see that the first element (1) matches the corresponding element (1) in the general form.

For the second element of the first row (x) to match the dilation factor (k) in the general form, it must be equal to k.

Comparing the second row of the given matrix with the general form, we see that the first element (3) matches the corresponding element (h) in the general form.

For the second element of the second row (4) to match the dilation factor (1) in the general form, it must be equal to 1.

So, based on the comparison, we can conclude that x = k = 1 and h = 3.

Hence, the values of x that would make the given matrix equal to a shear-dilation are x = 1.