Let

A=[−352−543−251], and B=[10−4−244−11−1].

Which of the following options is −3ABT?

Question

Let

A=[−352−543−251], and B=[10−4−244−11−1].

Which of the following options is −3ABT?

BlackTom AI · Accepted Answer

Question restatement: The problem provides A as a 3x3 matrix A = [ [-3, 5, 2], [-5, 4, 3], [-2, 5, 1] ] and B as a 3x3 matrix B = [ [1, 0, -4], [-2, 4, -1], [1, -1, -1] ]. The task is to determine which of the given options equals −3 A B^T. The answer options field in the data is empty, but there is a single option listed in the answer field: "[33−102−1851−114−1818−84−18]". Since the option formatting is ambiguous (it looks like a flattened 3x3 matrix with no clear separators), we will first compute −3 A B^T directly, then compare with the provided option when possible.

Step-by-step calculation plan:
- Compute the transpose B^T of B.
- Multiply A by B^T to obtain M = A B^T.
- Multiply the result by −3 to obtain N = −3 M.
- Check if the resulting matrix N matches the numeric pattern of the provided option string. If the option string cannot be parsed reliably, note the mismatch and explain the comparison limitations.

Computation (assuming the interpreted entries above):
- A = [ [-3, 5, 2], [-5, 4, 3], [-2, 5, 1] ]
- B = [ [1, 0, -4], [-2, 4, -1], [1, -1, -1] ]
- B^T = [ [1, -2, 1], [0, 4, -1], [-4, -1, -1] ]
- M = A B^T, computed by standard matrix multiplication:
  Row 1 of A dotted with columns of B^T gives: [-3,5,2]·[1,-2,1] = -11, [-3,5,2]·[0,4,-1] = 18, [-3,5,2]·[-4,-1,-1] = 5
  Row 2 of A dotted with columns of B^T gives: [-5,4,3]·[1,-2,1] = -10, [-5,4,3]·[0,4,-1] = 13, [-5,4,3]·[-4,-1,-1] = 13
  Row 3 of A dotted with columns of B^T gives: [-2,5,1]·[1,-2,1] = -11, [-2,5,1]·[0,4,-1] = 19, [-2,5,1]·[-4,-1,-1] = 2
  Thus M = [ [-11, 18, 5], [-10, 13, 13], [-11, 19, 2] ]
- N = −3 M = [ [33, -54, -15], [30, -39, -39], [33, -57, -6] ]

Now, evaluating the provided option string: "[33−102−1851−114−1818−84−18]". The sequence of numbers appears to be intended as the 3x3 entries arranged in row-major order, but the minus signs and lack of clear separators make parsing ambiguous. If we attempt to segment it as 9 entries in row-major form, a plausible interpretation could be:
- 33, −10, −18, 51, −11, −14, −18, −8, −18
or some other grouping depending on where the minus signs are intended. None of these clearly match the computed N = [ [33, -54, -15], [30, -39, -39], [33, -57, -6] ].

Key observations:
- The clearly computed result from the standard interpretation of A and B does not align with a straightforward reading of the provided option string, which already suggests a mismatch.
- Even if the option string were parsed with alternate spacings, the numeric values in the option do not coincide with the −3 A B^T result obtained above for the assumed matrices. This indicates either a mismatch in the interpreted B matrix (if the original B has different entries) or an inconsistency in the provided option formatting.

Potential sources of confusion or error to watch for:
- Ambiguity in the formatting of the matrix B in the prompt (the string "B=[10−4−244−11−1]" could encode different 3x3 layouts depending on where zeroes and separators are intended).
- The answer option formatting lacks clear delimiters, making exact numeric parsing uncertain.
- If the original problem uses a different B (or a different parsing of A or B), the resulting −3 A B^T would change accordingly; thus, without a precise, unambiguous matrix, a definitive option match cannot be confirmed.

In summary, with the interpreted A and B, the computed −3 A B^T is the matrix [[33, -54, -15], [30, -39, -39], [33, -57, -6]], which does not neatly align with the provided option string as it stands. Given the ambiguity in the option formatting, a definitive match cannot be asserted without a clarified, unambiguous option representation.

MATH1061/1002/1021 (ND) MATH1061 Canvas Quiz 7

Let A=[−352−543−251], and B=[10−4−244−11−1]. Which of the following options is −3ABT?

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MATH1061/1002/1021 (ND) MATH1061 Canvas Quiz 7

Let A=[−352−543−251], and B=[10−4−244−11−1]. Which of the following options is −3ABT?

查看解析

登录即可查看完整答案

类似问题

Vector a = 10 12 And vector b = 2 3 Whats the value of a*b ? (* is matrix multiplication); Please enter a number with no decimals.

Define the matrices A=\left[\begin{array}{ccc} 2&3\\ {1}&{-5}\end{array}\right] and B=\left[\begin{array}{ccc} 4&3&6\\ {1}&2.8&3\end{array}\right]. What is the entry in the first row and second column of AB?

Consider the matrix: \[ \mathbf {X=}\begin {pmatrix} 1 & 0 & 0 \\ 1 & 1 & 0 \\ 1 & 1 & 0 \\ 1 & 0 & 1 \end {pmatrix}.\]Which one of the following matrices is \(\mathbf {X}’\mathbf {X}\)?

Let \( A = \begin{bmatrix} 2 & -1 \\ -3 & -4 \end{bmatrix}\), \( B = \begin{bmatrix} -2 & 0 \\ -1 & 3 \end{bmatrix}\).Which of the following statements is correct?

Let \( A = \begin{bmatrix} 2 & -1 \\ -3 & -4 \end{bmatrix}\), \( B = \begin{bmatrix} -2 & 0 \\ -1 & 3 \end{bmatrix}\).Which of the following statements is correct?

If A=[54−34−1−300−5], then which of the following is A2?

更多留学生实用工具

希望你的学习变得更简单

Vector a = 10 12 And vector b = 2 3 Whats the value of ab ? ( is matrix multiplication); Please enter a number with no decimals.