Question

[M] For block operations, it may be necessary to access or enter submatrices of a large matrix. Describe the functions or commands of your matrix program that accomplish the following tasks. Suppose A is a \(20 \times 30\) matrix.

1. Display the submatrix of Afrom rows 15 to 20 and columns 5 to 10.
2. Insert a \(5 \times 10\) matrix B into A, beginning at row 10 and column 20.
3. Create a \(50 \times 50\) matrix of the form \(B = \left[ {\begin{array}{*{20}{c}}A&0\\0&{{A^T}}\end{array}} \right]\).

[Note: It may not be necessary to specify the zero blocks in B.]

Short answer

1. \( > > {\mathop{\rm A}\nolimits} \left( {15:20,\,\,5:10} \right)\)
2. \( > > {\mathop{\rm A}\nolimits} \left( {10:14,20:29} \right) = {\mathop{\rm B}\nolimits} ;\)
3. \[ > > {\mathop{\rm B}\nolimits} = \left[ {{\mathop{\rm A}\nolimits} \,\,{\mathop{\rm zeros}\nolimits} \left( {30,20} \right);\,\,{\mathop{\rm zeros}\nolimits} \left( {20,30} \right)A'} \right];\]

Step-by-step solution

Display the submatrix of A from rows 15 to 20 and columns 5 to 10

a)

Use the MATLAB code to display the submatrix of A from rows 15 to 20, as shown below:

\( > > {\mathop{\rm A}\nolimits} \left( {15:20,\,\,5:10} \right)\)

Insert a \(5 \times 10\) matrix B into A

b)

Use the MATLAB code to insert a\(5 \times 10\)matrix B into A as shown below:

\( > > {\mathop{\rm A}\nolimits} \left( {10:14,20:29} \right) = {\mathop{\rm B}\nolimits} ;\)

Create a \(50 \times 10\) matrix

c)

Use the MATLAB code to build matrix \(B\)out of four blocks, as shown below:

\[ > > {\mathop{\rm B}\nolimits} = \left[ {{\mathop{\rm A}\nolimits} \,\,{\mathop{\rm zeros}\nolimits} \left( {30,20} \right);\,\,{\mathop{\rm zeros}\nolimits} \left( {20,30} \right)A'} \right];\]