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I do not know what to do at all with this number. Any help would be greatly appreciated.

Let vector x = <x_1, x_2> , vector y = <y_1, y_2, y_3> and vector z = <z_1, z_2>.

Say that the systems

x_1 = 2y_1 + 3y_2 - 5y_3

x_2 = -3y_1 - 4y_2 + 2y_3

and

y_1 = 2z_1 - 3z_2

y_2 = 3z_1 - z_2

y_3 = z_1 + z_2

(a) Rewrite these linear systems as matrix equations involving vector x, vector y, vector z.

(b) Use the matrix product to write vector x in terms of vector z.

The 1st one would be written as

2 3 -5 1

-3 -4 2 1

where the 1st column is for y_1, the 2nd column is for y_2, the third column is for y_3,

and the last column is for the vector x.

The 2nd one would be written as

2 -3 1

3 -1 1

1 2 1

where the 1st column is for z_1, 2nd column is for z_2, and 3rd column is for the vector y.

Put the expression for y_1, y_2, and y_3 in terms of z_1 and z_2 into the 1st equations.

That is, x_1 = 2(2z_1 - 3z_2) + 3(3z_1 - z_2) - 5(z_1 + z_2).

Multiply it out on the right and combing the terms of z_1 and z_2.

In a similar fashion, work on the 2nd equation for x in terms of y by again substituting the bottom equations for y into the top equation for x_2.

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