Find the QRdecomposition of the given matrix where possible

Find the QR-decomposition of the given matrix, where possible (with one additional empty sheet after this page for your work): A = [0 -1 1 1 1 -1 0 1 1 0 -1 -1]

Solution

orthogonal matrix (Q) and an upper triangular matrix (R) using QR Decomposition method

A = QR,

where Q is an orthogonal matrix (its columns are orthogonal unit vectors meaning QTQ = I) and

R is an upper triangular matrix.

Matrix Q:
0.0000 0.5774 -0.8165 -0.0000
-1.0000 0.0000 0.0000 0.0000
0.0000 -0.5774 -0.4082 0.7071
0.0000 0.5774 0.4082 0.7071

Matrix R:
-1.0000 -1.0000 1.0000
0.0000 -1.7321 -0.5774
0.0000 0.0000 -1.6330
0.0000 0.0000 0.0000