. 2. 3. Student: _____________________ Date: _____________________ Instructor: Hugo Van hamme Course: Toegepaste Algebra 24-25: groep A Assignment: Hoofdstuk 1 ID: 1.2.35 Suppose a coefficient matrix for a system has pivot columns. Is the system consistent? Why or why not?6 × 8 six Choose the correct answer below. A. There is at least one row of the coefficient matrix that does not have a pivot position. This means the augmented matrix, which will have columns, could have a row of the form , so the system could be inconsistent. nine 0 0 0 0 0 0 0 0 1 B. There is a pivot position in each row of the coefficient matrix. The augmented matrix will have columns and will not have a row of the form , so the system is consistent. seven 0 0 0 0 0 0 1 C. There is a pivot position in each row of the coefficient matrix. The augmented matrix will have columns and will not have a row of the form , so the system is consistent. nine 0 0 0 0 0 0 0 0 1 D. There is at least one row of the coefficient matrix that does not have a pivot position. This means the augmented matrix, which will have columns, must have a row of the form , so the system is inconsistent. nine 0 0 0 0 0 0 0 0 1 ID: 1.3.17 Let a1 , a2 , and b . For what value(s) of h is b in the plane spanned by a1 and a2?= 1 4 − 1

− 7 − 23 2

3 − 3 h The value(s) of h is(are) . (Use a comma to separate answers as needed.) ID: 1.4.42 Could a set of three vectors in span all of ? Explain. What about n vectors in when n is less than m?ℝ4 ℝ4 ℝm Could a set of three vectors in span all of ? Explain. Choose the correct answer below.ℝ4 ℝ4 A. Yes. Any number of vectors in will span all of .ℝ4 ℝ4 B. Yes. A set of n vectors in can span when n m. There is a sufficient number of rows in the matrix A formed by the vectors to have enough pivot points to show that the vectors span . ℝm ℝm < ℝm C. No. There is no way for any number of vectors in to span all of .ℝ4 ℝ4 D. No. The matrix A whose columns are the three vectors has four rows. To have a pivot in each row, A would have to have at least four columns (one for each pivot). Could a set of n vectors in span all of when n is less than m? Explain. Choose the correct answer below.ℝm ℝm A. Yes. A set of n vectors in can span if n m. There is a sufficient number of rows in the matrix A formed by the vectors to have enough pivot points to show that the vectors span . ℝm ℝm < ℝm B. No. Without knowing values of n and m, there is no way to determine if n vectors in will span all of .ℝm ℝm C. Yes. Any number of vectors in will span all of .ℝm ℝm D. No. The matrix A whose columns are the n vectors has m rows. To have a pivot in each row, A would have to have at least m columns (one for each pivot)