For the following system of equations determine: (a) whether the system is consi

Question

For the following system of equations determine: (a) whether the system is consistent or inconsistent, why or why not? (b) if it is consistent, solve it. Make sure to identify the rank of the coefficient matrix, and, free and basic variables, (c) Write your solution in the vector form x = xp + xh, where xp is a particular solution and xh is the homogeneous solution. The augmented matrix of a linear system has been partially reduced by row operations to the form shown below. Continue the appropriate row operations and describe the solution set, if it exists, of the original system. Determine if 6 is a linear combination of vectors formed from the columns of the matrix A. Explain your answer. Without computing the matrix product ABC below, determine: (a) the dimensions of product. matrix ABC; (b) the second row of ABC. Do not compute the whole product.

Explanation / Answer

3) A matrix is of the dimension (5*2)

B matrix is of the dimension (5*1)

X should be of an dimensionsuch that (5*2) X (a*b) = (5*1)

X matrix is of the dimension (2*1)

For linear combination,

1*p + (-4)*q = 3

0*p + 3*q = 7 ==> q = 7/3

So, p = 3 + 4*7/3 = 37/3

But this value don't satisfy other equations

So, linear combination is not possible

4) A matrix is of the dimension (2*3)

B matrix is of the dimension (3*3)

C matrix is of the dimension (3*4)

ABC matrix is of dimension (2*3) X (3*3) X (3*4) = (2*4)

b) AB matrix is of dimension (2*3) X (3*3) = 2*3

Second row of AB -

3*0 + 5*2 + 0*0 = 10

3*1 + 5*0 + 0*0 = 3

3*0 + 5*1 + 0*4 = 5

Second row of AB has 3 columns.

Secon row of ABC

10*1 + 3*1 + 5*2 = 23

10*0 + 3*0 + 5* 0 = 0

10 * 3 + 3* (-1) + 5*5 = 52

10*0 + 3*0 + 5* 0 = 0

Second row of ABC has 4 columns.

Related Questions

Navigate

• Browse (All)
• Browse F
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.