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?

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BlackTom AI · Accepted Answer

We start by identifying the matrices given in the problem: A = [[2, -1], [-3, -4]] and B = [[-2, 0], [-1, 3]]. The question asks which statement is correct, and the provided answer option is c. $ -3A = \begin{bmatrix} -6 & 3 \ 9 & 12 \end{bmatrix} $.

To verify this, perform scalar multiplication of A by -3: multiply each entry of A by -3.
- Top-left: -3 * 2 = -6
- Top-right: -3 * (-1) = 3
- Bottom-left: -3 * (-3) = 9
- Bottom-right: -3 * (-4) = 12
Thus, -3A = [[-6, 3], [9, 12]], which matches the given option.

If one were to consider other possible statements (not provided here), we would similarly check them by applying the appropriate matrix operations and comparing results. Since only option c is presented, we confirm that this computation is correct by direct entrywise multiplication. This also illustrates the general rule that multiplying a matrix by a scalar scales every element by that scalar.

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?

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类似问题

Let A=[2−1−3−4] A = \begin{bmatrix} 2 & -1 \\ -3 & -4 \end{bmatrix}, B=[−20−13] B = \begin{bmatrix} -2 & 0 \\ -1 & 3 \end{bmatrix}.Which of the following statements is correct?

The matrix \(N = \left[ {\begin{array}{{20}{c}}{43}\\{27}\end{array}} \right]\;\begin{array}{{20}{c}}{Males}\\{Females}\end{array}\) lists the number of males and females in a group of 70 people. The matrix P that lists the percentage of males and females in the same group of people is given by:

The matrix \(N = \left[ {\begin{array}{{20}{c}}{43}\\{27}\end{array}} \right]\;\begin{array}{{20}{c}}{Males}\\{Females}\end{array}\) lists the number of males and females in a group of 70 people. The matrix P that lists the percentage of males and females in the same group of people is given by:

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A product has a selling price of $20, a contribution margin ratio of 40% and fixed cost of $120,000. To make a profit of $30,000. The number of units that must be sold is: Type the number without $ and a comma. Eg: 20000

Which of the following statement regarding cost is correct:

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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?

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类似问题

Let A=[2−1−3−4] A = \begin{bmatrix} 2 & -1 \\ -3 & -4 \end{bmatrix}, B=[−20−13] B = \begin{bmatrix} -2 & 0 \\ -1 & 3 \end{bmatrix}.Which of the following statements is correct?

The matrix \(N = \left[ {\begin{array}{*{20}{c}}{43}\\{27}\end{array}} \right]\;\begin{array}{*{20}{c}}{Males}\\{Females}\end{array}\) lists the number of males and females in a group of 70 people. The matrix P that lists the percentage of males and females in the same group of people is given by:

The matrix \(N = \left[ {\begin{array}{*{20}{c}}{43}\\{27}\end{array}} \right]\;\begin{array}{*{20}{c}}{Males}\\{Females}\end{array}\) lists the number of males and females in a group of 70 people. The matrix P that lists the percentage of males and females in the same group of people is given by:

In a consumer society, many adults channel creativity into buying things

Economic stress and unpredictable times have resulted in a booming industry for self-help products

People born without creativity never can develop it

A product has a selling price of $20, a contribution margin ratio of 40% and fixed cost of $120,000. To make a profit of $30,000. The number of units that must be sold is: Type the number without $ and a comma. Eg: 20000

Which of the following statement regarding cost is correct:

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希望你的学习变得更简单

The matrix \(N = \left[ {\begin{array}{{20}{c}}{43}\\{27}\end{array}} \right]\;\begin{array}{{20}{c}}{Males}\\{Females}\end{array}\) lists the number of males and females in a group of 70 people. The matrix P that lists the percentage of males and females in the same group of people is given by:

The matrix \(N = \left[ {\begin{array}{{20}{c}}{43}\\{27}\end{array}} \right]\;\begin{array}{{20}{c}}{Males}\\{Females}\end{array}\) lists the number of males and females in a group of 70 people. The matrix P that lists the percentage of males and females in the same group of people is given by: