Question

(Mid Term, Marks = 2, Lesson No. )

If \( A = \begin{bmatrix} 2 & 1 \\ 3 & 2 \\ \end{bmatrix} \) and \( B = \begin{bmatrix} 3 \\ 2 \\ \end{bmatrix} \), then compute AB?

Answer:

Question

(Mid Term, Marks = 2, Lesson No. )

If \( A = \begin{bmatrix}\begin{array}{cc|cc} 1 & 3 & 2 & 4 \\ \hline 2 & 4 & 1 & 3 \\ 5 & 3 & 2 & 4 \\ \hline 9 & 8 & 6 & 5 \\ \end{array}\end{bmatrix} \), then make a partition of \( B = \begin{bmatrix} 2 & 1 \\ 1 & 3 \\ 3 & 6 \\ 4 & 5 \\ \end{bmatrix} \) so that AB must be possible.

Answer:

Question

(Mid Term, Marks = 3, Lesson No. )

If \( A = \begin{bmatrix} 2 & -4 & -3 \\ 3 & 4 & -5 \\ \end{bmatrix} \) and \( B = \begin{bmatrix} 4 & -5 & -6 \\ 2 & 7 & 10 \\ \end{bmatrix} \), then calculate \( (A+B)^t \).

Answer:

Question

(Mid Term, Marks = 3, Lesson No. )

Construct partitions of the following matrix into three 2 × 2 blocks: $$ B = \begin{bmatrix} 1 & 2 & 3 & 4 & 1 & 3 \\ 3 & 4 & 5 & 6 & 3 & 4 \\ \end{bmatrix} $$

Answer:

Question

(Mid Term, Marks = 5, Lesson No. )

Show that the transformation \(L : R^3 \rightarrow R^2 \) definrd by \( L(x, y, z) = (2y+z, x) \) is linear?

Answer:

Question

(Mid Term, Marks = 5, Lesson No. )

Find an LU-decomposition of the matrix \( A = \begin{bmatrix} 2 & 3 \\ 5 & 7 \\ \end{bmatrix} \).

Answer:

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