Suppose A is a 3 x 3 matrix and det(A) = 5 If A = 2B, then what is the value of det (B)? Calculate the determinant of 4 x 7 √2 030x 002 √2 000 5
Suppose A is a 3 x 3 matrix and det(A) = 5 If A = 2B, then what is the value of det (B)? Calculate the determinant of 4 x 7 √2 030x 002 √2 000 5
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![**Matrix Determinant Questions**
1. Suppose \( A \) is a \( 3 \times 3 \) matrix and \(\det(A) = 5\). If \( A = 2B \), then what is the value of \(\det(B)\)?
[Answer Box]
2. Calculate the determinant of the following \( 4 \times 4 \) matrix:
\[
\begin{bmatrix}
4 & \pi & 7 & \sqrt{2} \\
0 & 3 & 0 & x \\
0 & 0 & 2 & \sqrt{2} \\
0 & 0 & 0 & 5
\end{bmatrix}
\]
[Answer Box]
**Guidance for Calculations:**
- For the first question, recall the property of determinants with respect to scalar multiplication: \(\det(cB) = c^n \cdot \det(B)\) where \(c\) is a scalar and \(n\) is the order of the matrix.
- For the second question, note that the matrix is upper triangular. For upper triangular matrices, the determinant is the product of the diagonal elements.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8eeaacd3-f9c7-4223-a8e6-a717e551a98a%2F4053f458-ab24-4b50-8e1f-3b9c28df6294%2Fm941tq_processed.png&w=3840&q=75)
Transcribed Image Text:**Matrix Determinant Questions**
1. Suppose \( A \) is a \( 3 \times 3 \) matrix and \(\det(A) = 5\). If \( A = 2B \), then what is the value of \(\det(B)\)?
[Answer Box]
2. Calculate the determinant of the following \( 4 \times 4 \) matrix:
\[
\begin{bmatrix}
4 & \pi & 7 & \sqrt{2} \\
0 & 3 & 0 & x \\
0 & 0 & 2 & \sqrt{2} \\
0 & 0 & 0 & 5
\end{bmatrix}
\]
[Answer Box]
**Guidance for Calculations:**
- For the first question, recall the property of determinants with respect to scalar multiplication: \(\det(cB) = c^n \cdot \det(B)\) where \(c\) is a scalar and \(n\) is the order of the matrix.
- For the second question, note that the matrix is upper triangular. For upper triangular matrices, the determinant is the product of the diagonal elements.
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