Matrices and determinants

2000017103

Level: 
B
Compute the inverse matrix to the matrix: \[ \left (\array{ 1& 0 & 0\cr 0 & 1 & 1 \cr -1& 0 & 1} \right ) \]
\[ \left (\array{ 1& 0 & 0\cr -1 & 1 & -1 \cr 1& 0 & 1 } \right ) \]
\[ \left (\array{ 1& 0 & 0\cr 1 & 1 & 1 \cr 1& 0 & 1 } \right ) \]
\[ \left (\array{ 1& 0 & 0\cr 1 & 1 & 1 \cr -1& 0 & -1 } \right ) \]
\[ \left (\array{ -1& 0 & 0\cr -1 & 1 & -1 \cr 1& 0 & -1 } \right ) \]

2000017102

Level: 
B
Compute the inverse matrix to the matrix: \[ \left (\array{ 4& 3 & 0\cr 2 & 1 & 2 \cr 0& 0 & -1 } \right ) \]
\[ \left (\array{ -\frac12& \frac32 & 3\cr 1 & -2 & -4 \cr 0& 0 & -1 } \right ) \]
\[ \left (\array{ \frac12& \frac32 & 3\cr 1 & -2 & -4 \cr 0& 0 & 1 } \right ) \]
\[ \left (\array{ -\frac12& \frac32 & -3\cr -1 & -2 & -4 \cr 0& 0 & -1 } \right ) \]
\[ \left (\array{ -\frac12& \frac32 & 3\cr 1 & 2 & -4 \cr 0& 0 & -1 } \right ) \]

2010006701

Level: 
A
Identify a true statement related to the following matrix \(A\). \[ A = \left (\array{ 2& 4 & -3& 7\cr 9 & -5 & -1 & 8 \cr 11& 0 & 8& 12 \cr -7 & -8 & 1& 13 \cr 9& 10 & -6& 2 } \right ) \]
\(A\) is a \(5\times 4\) matrix and \(a_{(2,\, 3)} = -1\).
\(A\) is a \(5\times 4\) matrix and \(a_{(2,\, 3)} = 0\).
\(A\) is a \(4\times 5\) matrix and \(a_{(2,\, 3)} = 0\).
\(A\) is a \(4\times 5\) matrix and \(a_{(2,\, 3)} = -1\).

9000019903

Level: 
A
Identify a true statement related to the following matrix \(A\). \[ A = \left (\array{ -2& 3 & 10& 5 & -5\cr 6 & 11 & -7 & 2 & -3 \cr -7& 15& -6& 2 & 4\cr -8 & 1 & 13 & -5 & 0 } \right ) \]
\(A\) is a \(4\times 5\) matrix and \(a_{(3,\, 2)} = 15\).
\(A\) is a \(4\times 5\) matrix and \(a_{(2,\, 3)} = 15\).
\(A\) is a \(5\times 4\) matrix and \(a_{(3,\, 2)} = -7\).
\(A\) is a \(5\times 4\) matrix and \(a_{(3,\, 2)} = 15\).