Find x1 and x2.

left bracket Start 2 By 2 Matrix 1st Row 1st Column negative 4 2nd Column 1 2nd Row 1st Column 5 2nd Column 4 End Matrix right bracket left bracket Start 2 By 1 Matrix 1st Row 1st Column x 1 2nd Row 1st Column x 2 End Matrix right bracket plus left bracket Start 2 By 1 Matrix 1st Row 1st Column 11 2nd Row 1st Column negative 19 EndMatrix right bracket equals left bracket Start 2 By 1 Matrix 1st Row 1st Column negative 11 2nd Row 1st Column 40 End Matrix right bracket

[tex]\left[\begin{array}{ccc}-4&1\\5&4\\\end{array}\right] \times \left[\begin{array}{ccc}x_1\\x_2\\\end{array}\right] + \left[\begin{array}{ccc}11\\-19\\\end{array}\right] = \left[\begin{array}{ccc}-11\\40\\\end{array}\right][/tex]

Step 1

Multiply first 2 x 2 matrix with 2 x 1 vector, we get

[tex]\left[\begin{array}{ccc}-4x_1&+ x_2\\5x_1&+ 4x_2\\\end{array}\right] + \left[\begin{array}{ccc}11\\-19\\\end{array}\right] = \left[\begin{array}{ccc}-11\\40\end{array}\right][/tex]

Step 2

Add the 2 x 1 matrices on LHS, we get

[tex]\left[\begin{array}{ccc}-4x_1&+x_2&+11\\5x_1&+4x_2&-19\\\end{array}\right] = \left[\begin{array}{ccc}-11\\40\end{array}\right][/tex]

Step 3,

we get

[tex]-4x_1 + x_2 + 11 = -11[/tex]

and

[tex]5x_1 + 4x_2-19=40[/tex]

Step 4,

Simplify, we get

[tex]-4x_1+x_2=-22----(1)\\ 5x_1+4x_2=59----(2)[/tex]

Step 5,

multiply eqn(1) by 4

we get

[tex]16x_1+4x_2=-88[/tex]

Step 6,

eqn (2) - eqn(3)

we get

[tex]21x_1 = 147\\x_1 =\frac{147}{21} \\x_1= 7[/tex]

substituting in eqn (1), we get

[tex](-4 \times 7) + x_2 = -22[/tex]

so, we get

[tex]x_2 = 6[/tex]

Therefore

[tex]x_1 = 7\\x_2 = 6[/tex]