aflacatn
2021-02-24
Answered

Write importance and rule for partitioning of matrix.

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Gennenzip

Answered 2021-02-25
Author has **96** answers

Step 1 Rule of partitioning of matrix.

Large matrices can be partitioned using a system of horizontal and vertical (dashed) lines.

Clearly a given matrix can be divided into blocks in different ways.

For example, the following

where E,F,G,H,I and J are the arrays indicated by dashed lines.

The above matrix can also be partitioned as,

This shows that a matrix can be partitioned in many ways, but the new blocks can be of different size and different order.

The matrix entries of such a partitioned matrix are called submatrices or blocks. The main matrix is often referred to as super matrix.

Step 2 Importance for partitioning of matrix.

Partitioning of matrices is useful when it is applied to very large matrices because the operations can be carried out easily on the smaller blocks of the matrices. On operating the partitioned matrices, the basic rule can be applied to the blocks as though they were single elements.

If M is a square block matrix such that the non diagonal blocks are all zero matrices, i.e.

The importance of block diagonal matrix is that the algebra of the block matrix is frequently reduced to the algebra of the individual blocks. Suppose f(x) is a polynomial and M is the above mentioned block diagonal matrix. Then f(M) is a block diagonal matrix and

Jeffrey Jordon

Answered 2022-01-24
Author has **2313** answers

Answer is given below (on video)

asked 2021-02-08

Let B be a 4x4 matrix to which we apply the following operations:

1. double column 1,

2. halve row 3,

3. add row 3 to row 1,

4. interchange columns 1 and 4,

5. subtract row 2 from each of the other rows,

6. replace column 4 by column 3,

7. delete column 1 (column dimension is reduced by 1).

(a) Write the result as a product of eight matrices.

(b) Write it again as a product of ABC (same B) of three matrices.

1. double column 1,

2. halve row 3,

3. add row 3 to row 1,

4. interchange columns 1 and 4,

5. subtract row 2 from each of the other rows,

6. replace column 4 by column 3,

7. delete column 1 (column dimension is reduced by 1).

(a) Write the result as a product of eight matrices.

(b) Write it again as a product of ABC (same B) of three matrices.

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Find a basis for the space of $2\times 2$ diagonal matrices.

$\text{Basis}=\{\left[\begin{array}{cc}& \\ & \end{array}\right],\left[\begin{array}{cc}& \\ & \end{array}\right]\}$

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find the product of the vectors v= 2i-3j+k and vector w = 2i+j+k

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Find the number of irrational roots of the equation

$\frac{4x}{{x}^{2}+x+3}}+{\displaystyle \frac{5x}{{x}^{2}-5x+3}}=-{\displaystyle \frac{3}{2}}.$

$\frac{4x}{{x}^{2}+x+3}}+{\displaystyle \frac{5x}{{x}^{2}-5x+3}}=-{\displaystyle \frac{3}{2}}.$

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Simplify this expression with $\mathrm{cos}$ and $\mathrm{sin}$

$\frac{\mathrm{cos}12x}{\mathrm{cos}4x}-\frac{\mathrm{sin}12x}{\mathrm{sin}4x}=\frac{{\mathrm{cos}}^{2}6x-{\mathrm{sin}}^{2}6x}{{\mathrm{cos}}^{2}2x-{\mathrm{sin}}^{2}2x}-\frac{2\mathrm{sin}6x\mathrm{cos}6x}{2\mathrm{sin}2x\mathrm{cos}2x}$

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Set containing numbers $1$ to $49:\{1,2,3,\cdots ,49\}Now,\; I\; want\; to\; divide\; the\; set\; into$ 7$subsets\; such\; that\; each\; subset\; should\; contain$ 7$elements\; and\; sum\; of\; the\; elements\; of\; each\; subset\; should\; be$ 175$.$

Is it possible to prove that such subsets exist?

Is it possible to prove that such subsets exist?

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compute the indicated matrices (if possible).

Let