Holooly Plus Logo
Holooly Plus Logo

Question 3.1.15: Calculate [ 2 3 0 1 4 1 2 1 0 0 0 1][3 1 1 2 2 3 0 5].

Calculate \left [ \begin{matrix} 2 & 3 & 0 & 1 \\ 4 & 1 & 2 & 1 \\ 0 & 0 & 0 & 1 \end{matrix} \right ] \left [ \begin{matrix} 3 & 1 \\ 1 & 2 \\ 2 & 3 \\ 0 & 5 \end{matrix} \right ] .

The Blue Check Mark means that this solution has been answered and checked by an expert. This guarantees that the final answer is accurate.
Learn more on how we answer questions.

We have

\left [ \begin{matrix} 2 & 3 & 0 & 1 \\ 4 & 1 & 2 & 1 \\ 0 & 0 & 0 & 1 \end{matrix} \right ] \left [ \begin{matrix} 3 & 1 \\ 1 & 2 \\ 2 & 3 \\ 0 & 5 \end{matrix} \right ] =\left [ \begin{matrix} 2(3)+3(1)+0(2)+1(0) & 2(1)+3(2)+0(3)+1(5) \\ 4(3)+1(1)+2(2)+1(0) & 4(1)+1(2)+2(3)+1(5) \\ 0(3)+0(1)+0(2)+1(0) & 0(1)+0(2)+0(3)+1(5) \end{matrix} \right ] \\ =\left [ \begin{matrix} 9 & 13 \\ 17 & 17 \\ 0 & 5 \end{matrix} \right ]

Related Answered Questions

Calculate [2 3 4 1][5 1 -2 7].

Verified Answer:
Taking dot products of the rows of the first matri...

Perform the following operations. (a) [2 3 4 1] + [5 1 -2 7] (b) [3 0 1 -5] – [1 -1 -2 0] (c) 5[2 3 4 1] (d) 2[1 3 0 -1] + 3[4 0 1 2]

Verified Answer:
(a)    \left [ \begin{matrix} 2 & 3 \\ ...

Let B = [2 1 -1 -4 3 3 6 8 -3] and b = [3 -13 4]. Use an LU-decomposition of B to solve Bx = b.

Verified Answer:
In Example 3.7.2 we found an LU-decomposition of B...

Let A = [1 1 1 -1 -2 3 -2 -4 6] and b = [1 6 12]. Use an LU-decomposition to solve Ax = b.

Verified Answer:
We first find an LU-decomposition for A. Row reduc...

Find the inverse of each of the following elementary matrices. Check your answer by multiplying the matrices together. (a) E1 = [1 2 0 1] (b) E2 [0 0 1 0 1 0 1 0 0] (c) E3 = [1 0 0 0 1 0 0 0 -3]

Verified Answer:
The inverse matrix E_{1} ^ {-1} is ...

Find the 2 × 2 elementary matrix corresponding to each row operation by performing the row operation on the 2 × 2 identity matrix. (a) R2- 3R1 (b) 3R2 (c) R1 ↑↓ R2

Verified Answer:
For (a) we have \left [ \begin{matrix} 1 &a...

Let E1 = [1 0 0 2 1 0 0 0 1], E2 = [1 0 0 0 1 0 0 0 3], and A = [1 1 3 0 -1 2 0 5 6]. Calculate E1A and E2E1A. Describe the products in terms of matrices obtained from A by elementary row operations.

Verified Answer:
By matrix multiplication, we get E_{1}A = \...

Let A = [1 2 1 2 4 4]. Find a sequence of elementary matrices E1, . . ., Ek such that Ek . . . E1A is the reduced row echelon form of A.

Verified Answer:
We row reduce A keeping track of our elementary ro...

Let A = [1 0 1 1 0 3 -1 1 -1]. Write A and A^-1 as products of elementary matrices.

Verified Answer:
Row reducing A to RREF gives \left [ \begin...

Find an LU-decomposition of A = [2 -1 4 4 -1 6 -1 -1 3].

Verified Answer:
Row reducing and keeping track of our row operatio...